Why not use a gable fan? Not costly, easy to install and keeps the air flowing very well. And the ones I've used have thermostats that control them according to your setting.

Best of luck.

gable vents have worked well for years.
most people make the mistake of mixing ventilation
stratagies.
there are 3 ways to ventilate an attic
1-gable end vents
2-soffit and ridge venting
3-soffit and passive venting..silver whirley bird vents.

power vents make more problems than they solve.
granted attic temps drop, but it is by pulling
conditioned air into attic through penetrations
between attic and conditioned space, or from leaky ducts.
I wouldn't recommend pav's for anyone..ok maybe a couple of
people (LOL!)

opening second floor into attic..just doesn't make sense to me..but I may have missed something.

best of luck.

There is a door to the upstairs that is kept closed (and that I'm going to weatherstrip too). Although the area is finished into two bedrooms and a bath, they are not going to be used because my cousin who lives there is disabled and won't be going up and down stairs. Other cousins and I have just finished getting stuff out of the upstairs area, so it's basically empty now. Since a new roof is needed, we're faced with the question of whether to put a ridge vent in. All the contractors I've gotten bids from have included it in their estimate. From the reading I've done, it seems a ridge vent needs soffit vents and a clear pathway under the sheating from the soffits to the ridge to work. There are no soffit vents. We could put in the Smartvent thing but there's still the problem of the insulation being packed into the rafters and no easy way to install baffle vents (because the finished walls and ceiling block access to the rafters). I'm starting to think maybe I should leave the ventilation like it is, just the gable vents, and we'll raise the upstairs windows in the summer.

The construction you have described is a no-go in this area. What is needed is air flow under the sheathing that holds the roofing material. That air flow cannot be addressed by gable vents, windows or fans. Its purpose is protection of building material, not creature comfort. Lack of same violates most material warranties.

"The insulation is stuffed in the rafters."

A space is needed above it for airflow-perhaps in your case the insulation is not full depth,allowing some flow.
Ridge venting will exhaust any hot air, so installation would be marginally useful.
A possible solution is putting down sleepers at each rafter and re-sheathing and roofing atop them. Sometimes called a "cold" roof, attention to detail can make it indistinguishable from the original and leaves the existing insulation intact.

A gable fan would be hard to install because the gables are up there behind the ceiling and walls. The only access to the eaves are the kneewall doors and there isn't much space behind them. We'd have to cut the ceiling to get up there to the gables.

The extra roof is an interesting idea. Would the sleepers run up and down the roof and create the pathway for the air? Or would they go across the roof? If they go across, wouldn't they then block the air pathways? Would the extra weight of another roof be a possible problem? How could I tell if the structure could handle sleepers and an extra roof? The present roof sheating is 1x4 boards, not plywood. I'm told there are some soft spots and some of the sheating is likely going to have to be replaced. There was a leaking problem in 1998 and roof repairs were done then, but I don't think they did anything to the sheating then.

Can baffles be put in from on top the roof after the top is cut off for the ridge vent? Could they slide in from there or do they tear up too easily? Are baffles ever made of anything besides foam?

The house has been there 56 years and the present roof has lasted 29, all without roof ventilation except for the gable vents, so I'm wondering why a new roof would start to have problems because of lack of ventilation. It's a pretty steep roof, if that makes any difference in this issue.

I'm going to use a light-colored shingle. There are mature shade trees in the yard, and one in particular shades it from the west. Virginia is hot in the summer, but in the winter it seldom gets below 20.

You might read up on some of these from building sciences on venting as well as non-venting. You also might want to look into radiant barrier installs that coincides with venting to reduce heat in the summer months.

radiant barrier info- http://www.energyconservationspecialists.com/

Here is a link that might be useful: building sciences

"Would the sleepers run up and down the roof and create the pathway for the air?" Yes.

"Would the extra weight of another roof be a possible problem? How could I tell if the structure could handle sleepers and an extra roof?" It could. Ultimately such a decision need be made by a competent individual, possibly an engineer.

1x4's are good sheathing. Your insulation may be in worse shape than you think. On the other hand, no one thought about tight building envelopes when it was built and there may be enough leakage that the typical weather sealing strategies haven't had a deleterious effect.

A metal roof could solve a number of problems here, i.e. enable an insulated cold roof, provide a radiant barrier and yet be of light weight.

I like the idea of a metal roof! Tell me how it should be done--what goes where in the various layers of constructing it. Can you point me to a website explaining "insulated cold roof"? Does a metal roof need ventilation? How would the ventilation work?

Strongly recommend reading at the link Sierraeast provided, and in general, anything by Joe Stiburek.
For particulars on metal roofing best contact the manufacturer.
Putting the roof on sleepers is fairly common, you'd need a contractor to dovetail with roof mfg.

I've found some other good material: an article on cool roofs, which discusses advantages of above sheathing ventilation. I'll put the URL below. Another article discusses in detail how to do an insulated cold roof. The URL for that one is:
http://danperkinsroof.com/1108_JCL_Perkins_A.pdf
I like the idea of having more insulation but I don't know about adding all that structure on top of the roof deck--the rafters would be supporting two rock decks plus other stuff (the sleepers) plus the roof itself.

The above sheathing ventilation wouldn't involve a lot of weight, so I'm very interested in pursuing that. Now to find a contractor who knows how to do it. The contractors I've been getting estimates from on an asphalt roof have all recommended a ridge vent without making any recommendations on creating intake vents or pathways to the ridge. I think they think if they put in a ridge vent, then they've done everything necessary for ventilation.

Here is a link that might be useful: cool roofs

When I told a contractor about my idea here on doing the above sheathing ventilation, he reminded me that it vents only the roof and doesn't vent the attic. The felt paper on top of the sheathing will be a vapor barrier and prevent the passage of moisture, and warm moist air would condense on the underside of the cold sheathing. I spoke to another contractor who does the ASV and she suggested doing soffits into the attic and the ridge vent could ventilate both the attic and roof at the same time. Or we could fill up attic spaces with foam insulation. There's no easy way to do soffits and baffles. What would happen if I cut through the peak into the attic to make the slot for a ridge vent but didn't do the soffits and baffles? Would that suffice as an escape hatch for moist air or will I have condensation problems? The moist air will have to work its way through the insulation batts stuffed in the rafters to get to the sheathing. There are two gable vents.

"The felt paper on top of the sheathing will be a vapor barrier and prevent the passage of moisture, and warm moist air would condense on the underside of the cold sheathing."

Quality energy detailing will put the vapor barrier where it prevents moist air from entering the building envelope. In a heating climate that is on the inside. Thermal transfer will take place (nothing's perfect) but not moisture transmission. Air tight drywall was one approch at such a barrier. There is also poly sheeting. Well done foam,another.
You have two issues, attic ventilation and roof venting. If the attic is part of the living space or acts as a thermal buffer between floor below and the roof, don't mix the two, i.e. attempt to vent attic and roof through the ridge. Insulate and provide vapor barrier. Roof venting needs address. If the attic will be unused and the floor is well insulated and has a vapor barrier, pull the insulation out of the rafters and forget about soffit and ridge vents. True, they provide additional venting, but 1x sheathing in an un-insulated attic won't be a problem. The existing windows (open) will assist.

When I first asked a contractor who'd given me a bid on asphalt shingles about a metal roof, he said it would be about $900 more than the price he quoted on the shingles. Great! But now he's talked to his metal roof guy and the cost per square would be $1100 and I'd need 20 squares, and $22,000 for a roof is entirely out of the question. I had no idea metal roofs would be that much more expensive. So now I'm back to the asphalt and I think I'm not going to do soffits and ridge. I'll just open the windows up there in the summer. That sounds like a good idea about adding insulation to the floor upstairs. Do you have to tear up the floor or can it be blown in? If it's blown, what do you do about a vapor barrier?

Can't comment on metal roof pricing, but at that number my eyebrows would be on the Hubble.
OTOH, metal roofs can have great longevity.
Blown in requires an entry and exit port, can be nozzle sized holes, could be done in the attic flooring. AIUI, the holes are plugged upon completion. Not an expert here, but some types are considered inherent vapor barriers.
Well sealed rooms (wallboard or plaster/lath) with a couple coats of latex paint usually suffice as VB for homes without excess humidity (long hot baths, boiling pasta every night without vent fans etc.)and/or abnormal positive pressures (poorly designed HVAC ).