I also would like to what sort of light I should use on my rosemary plant. I would prefer not to go the route of the tube type fluorescent, HSP or HID lights as my plant is sharing our livingroom, but I could use a compact fluorescent or grow light (what exact IS a grow light?) if it is recommended. Please advise.

Well, I was going to respond, but I don't have much good things to say about 'grow lights'. which I think are great for seedlings but not much else. They may HELP a wee bit, but you have to keep them really close to the plants.... I am not good at keeping herbs in the house as I can grow them outdoors all year in my zone. HID lights are great, but really expensive, If you have the $$ then go for it, but other than that... the 'grow lights would have to be inches over the rosemary and may block 'real' sunlight.
I don't know if your problems are from lack of sunlight, as most of the winter my sky is overcast, so sunlight doesn't help my rosemary.
You can get 'grow lights' are flourescents that you can get at places like Home Depot.

I have not had much luck with grow lights but I do use broad spectrum floresent lights to mimic the sun. The are the all purpose lights that are used by people that need additional light during the winter. They are closer to natural light than the bulbs labled "Grow Lights"

Keep cutting back your parsley and using the leaves. By removing leaves it should continue to grow. However the bad part of parsley is that it goes to seed the second year of growth and then dies. If you manage to keep it alive this winter place it in the ground in an area that you use no insectasides. Have your son watch for small black spots that keep getting bigger. These are butterfly larva and if you have enough leaves on the plant they will form butterflies. I do not know why they are attracted to the second year plants more than the first year ones but I have had few on the new plants while the older plants are eaten to the stub sticking out of the ground. Second year carrots are similar but more butterflies like the parsley.

Over the weekend, the parsley turned pale and got limp, so Sunday I bought a grow light at the local nursery and installed it. That seemed to kill of the parsley entirely, as it immediately went flat and started to dry up. The rosemary, on the other hand, keeps on growing happily and putting on new growth.

So Wednesday I trimmed back the parsley to an inch or two of stems. The petunias were still looking poorly, so I put them out on the porch to finish dying. The rosemary seems to love the new light.

Interesting that the parsley just wilted and dried up. Might be it was already too far gone, but maybe it was that it was struggling to adapt to the dark, indoor conditions and couldn't take the 'intense' light source that was introduced.

Might be fun to start some parsley from seed under the new light and see what happens.

Rosemary is hardy enough that you can leave it outside all year as long as the temps are above freezing. It can even take some light freezing. Normally in zone 4 you would have to keep in inside most of the winter, but the way things have been going this year, who knows?

It likes dry conditions and lots of light so I am sure it is happy as can be under the grow light. Good investment.