Barbara,
Wow! Your poor computer is in for major surgery. Replacing the mother board is akin to ripping open the human body, and replacing the brain, and most of the nervous system. The cost of the new mother board is not a major expense, (depending on where you buy it), but the labor can be expensive, since you have to pretty much "gut" the computer, in order to get to the mother board, and then afterwards, replace everything that you removed to get to it.
As much as Mr. L enjoys tinkering with things, if I were in his shoes, I would stop buying extended warranties, pocket the money, and repair those computers myself. It's not particularly difficult, (there are plenty of online information sites, and support boards), and the parts are usually not expensive, (if you buy them at the right places). The only hitch is that Dell uses a lot of proprietary hardware and software, which prevents their customer's from doing certain types of service on Dell computers, (of course, you can usually find the information that you need on internet discussion boards, and info sites). Because of the proprietary stuff, though, having a Dell makes your job about 10 times harder than it would be on virtually any other brand of computer. That's the main reason why I never buy any Dell computers, because I do all my own repair and maintenance work, and I resent a manufacturer intentionally making a product harder to service, than it would otherwise be. That's just ripping off the consumer.
My brother owns a Dell, and I've had to spend many hours trying to figure out how to get around some of Dell's BS in that computer, but so far, I've always been able to find a solution, and bring it back from the dead. I enjoy working on computers, but working on a Dell is frustrating as hell. The only good part about working on a Dell, is the immense sense of accomplishment you feel, when you finally solve the problem. It feels so good to stop beating your head against the wall.

That said, Dells are usually more reliable than most other brands of computers, but when you do have to work on them - look out.
I hope you get it going soon.
Luve,
Galahad