Well, aside from that little hiccup, everything seems to be going smooth. I've got Windows reinstalled now and I'm updating Kaspersky and downloading Firefox. Speed seems to have returned to normal and none of the drives or anything seem to be dropping out.
Other than getting a SATA DVD put in, I've made a few changes in cabling and added a few more cables to the power supply so each cable is shared less. The SATA hard drive and DVD share a cable (as the power supply only came with one SATA power cable with 2 ends on it). The IDE drive is on it's own power cable and IDE cable. The side, front, and rear case fans and the CPU cooler share a cable, and the video card is still on it's own cable.
Like I said, so far so good... although I still haven't isolated exactly what the issue was before. Not sure if it was the power supply or the Windows installation going out, but it's running fast and strong without issues for half an hour now, which is more than it was doing before. Anyway, thanks for all the help. I'll post back if it starts acting up again.