Well, the good news is that Bloodspite is my hero! He spent hours with me via IM this afternoon, helping me figure out exactly what was wrong with my desktop computer. The bad news is that one of the IDE ports is bad. This is causing fluctuating power problems for the other port. This is also messing with my hard drives, and explains why I have been going through hard drives like they're disposable. The good news is that the short I caused that finally shut things down after months of problems merely took out one of two unreliable IDE ports. So, I just made previously-intermittant problems permanent a bit sooner than they would've been. So... guilt free!
Bad news is that I need a new motherboard, a new processor, and a new (for the 4th time) hard drive... Ugh. Good news is that the peripherals, etc., are worth keeping for awhile, so it would cost less than an entirely new computer.
Thanks to all of you who advised me and helped me sort things out. It helped my decision process for the laptop purchase, and gave me the confidence to deal appropriately with the desktop when I'm ready. You're awesome!