Open Question: What could cause my laptop to not turn on?
I don't think there's any such thing as a "CMOS button" on a laptop, and anyway I doubt that it would cure this problem, because this sounds like a problem which almost certainly is caused by something that is physically broken.
I know you can't afford to fix your laptop - but you also can't afford to be without it, and your fiddling and wiggle can only make the problem worse. I suggest you seriously consider getting it fixed anyway - try a small local mom & pop repair place instead of a big place like Best Buy; it'll be cheaper for sure.
Open Question: Could I replace the video card on my laptop?
Sorry.
The Old Computer Guy
Open Question: What is the best case I could buy for $100 or less?
Mostly what you'd look for is good ventilation and fans. Other things can be nice too like tool-free expansion slots and drive bays, a cable management system (or get some zip-ties) and plenty of space inside.
NZXT, Apevia, Cooler Master, and of course Antec all make some decent cases. The NZXT Gamma is an example of a decent case for about $35. You'd want to add more fans to it and it's ugly as hell but it has plenty of places for air to get in and out.
