The new one is en route, and I've got my data backed up. So I thought I had nothing to lose.
New symptoms: the machine will turn on after I leave it unplugged for 10mins or so. Then it turns itself off again after 15mins of uptime or so. I'm going to check to see if my HSF is making good contact, but could it be anything else? It'd kind of suck if more than my HDD died in the last week.
Edit: That's 15mins of uptime with me trying to reinstall XP on an old HDD I had laying around.
Edit2: I've got 2 Y-molex power cables splitting the power to feed 1) GPU, 2) SATA, 3) IDE. The GPU shouldn't be doing much in a dos-ish environment, and I figured the HDD power draw would max out at startup and taper off afterwards. I guess I could be straining my PSU, but it's 350W and my system runs waay less than that. (My old PSU was a Seasonic 300W).
Edit3: I've also learned that letting it stay off but "powered" (PSU connected to outlet) for 3hrs is not enough time for it to recover. But letting it stay off unpowered for ~10mins or so is sufficient to get it going again. I suppose it's likely that my PSU isn't doing too well, but I kind of don't want to believe that a 2mo old PSU would die on me.
Edit4: I just remembered that I was in a rush putting in the second Y-molex adapter. (I needed it so that I could power both the SATA and IDE drives simultaneously.) All I had was a Y adapter that I had modded to split into 5v and 7v lines (for fan speed), so I pulled out the leads and put them back into the standard 12V configuration. What I didn't do was "reset" the clips so that the connectors would stay in place. Instead, I connected the wires and pushed the ends together if they came out the back. I've since removed the second Y adapter and am now attempting a reinstall while I finish fixing the Y-adapter. I also disconnected my SATA drive from power, so my PSU load *should* be the similar to what it was before I had these shutdowns.