If there are no seams, I would suspect that you are dealing with some sort of laminate. If you had solid wood, there would be an obvious, visible grain on the edges of each door.

Your cabinet description reminds me of cabinets I saw back in the late 60's or early 70's. They were made of particle board or MDF and were covered with some kind of wood looking plastic based coating which was heavily grained and dark in color. Where the stuff was worn you could see a sort of orange subsurface underneath.
I don't know if this is the same as yours or not.

Sounds like the cabinets they put in mobile homes and some manufactured homes. Kennebunker has it right I think.

I think they can be painted. You can try a bond test first, if you want to be sure you'll get a good bond. Since you once used Murphy's, be sure they are clean, well rinsed and dry before you paint.

Thanks for the replies. Kennebunker, Yesterday I asked a construction worker across the street who said they are MDF cabinets with veneer maple skin. That's really all he could tell me. I removed one of the doors and used a sander to sand the "skin" off which now shows a very light colored wood with a nice grain. Now I'm really confused. I read that MDF was just wood shavings & other crap glued together so why does it look like a very pretty oak cabinet? I'm thinking it might take me all summer to sand these but if they really are MDF is this what I want to do versus maybe buying bond gripper and then painting. Sorry for rambling but I'm just confused. Thanks for any help.

To see the base material, you can lightly sand one or more edges, until you have removed all the paint. At this point, you will either see what looks like wood grain, with a regular, repeated pattern, or you will see something more random.

goldensmom, you're right about mdf - it is just glue and wood bits. The veneer is actually a thin slice of wood - maple in your case. It's real wood and can be re-finished. But it's glued onto the mdf to make it appear like solid wood for a fraction of the price.

Should you refinish 30 year old veneered cabinets? I think it would be a monstrous chore, but you could do it. You would likely need to do some veneer replacement and to be honest, the finished product would not be nice enough to merit the work you'd put into it. MDF can expand when it gets wet and you never know what kind of problem you may find along the way.

If the grain is still there and the surface is smooth, I'd paint. Actually, I think painted cabs are more popular right now than naturally finished ones.

JMO, though, and if you have your heart set on refinishing them, you should!