Okay, after trying to do some spreadsheet work, things were not calculating properly, so, I shut everything down and went ahead and installed the new RAM. It booted right up, but, that's not unusual after the computer's been on for several hours. The true test will be tomorrow, after having the computer off all night, and then seeing if it boots right up on the first try.
My hard drive didn't show up this weekend, FedEx is really bad out where I live. Anyway, hoping it arrives tomorrow, then I'll install it and transfer files and programs, then... the next morning should tell a lot too.
Even if these two things solve this problem, I'm still going to go ahead and clean the CPU and order a new graphics card. Heck, may as well.
As mentioned earlier, if anyone can suggest a cheap graphic card that is a bit better than the one I have, anything will be better than this old one, I'm sure. I'd love suggestions.
And thank so much to all of you guys! You ROCK!!
OHHHH... one more thing. If the computer still has a problem booting up tomorrow morning, can I then assume it's not the RAM, and go ahead and install my removed RAM in the extra slots so I'll end up with 8GB total?