I'm with Canthearu. The CPU's core voltage is generated by voltage regulators near the CPU. It doesn't really matter a whole lot what the PSU does as long as those VRMs are healthy. Obviously if the PSU is TOO far out of tolerance, the VRMs won't be healthy, and then your CPU is at risk. But... my point is, there's a buffer. Those VRMs are fed from +12V, so if that rail is even in the ballpark of correct, your CPU is almost certainly A-OK.

Your RS-232 ports may be flaky, and any analog outs that use op-amps might suffer when the signal swings negative. (Pretty much a concern for analog audio outputs, maybe VGA depending on the DAC topology, since a video op-amp buffer would need to be able to hold 0V, which means the op-amp needs to have a negative rail just a little under that.)

All in all, there's no certainty in life. If you need to buy a new motherboard and PSU for your own peace of mind, then go for it. But I wouldn't. I would just run some stress tests, and if it works OK, then it is OK. On one hand, you may blow up all three components. On the other, you may blow up zero of them. Or lightning could strike and take them all out regardless what you do. Who knows? 😀

I am now using HWMonitor instead of SpeedFan to get PSU voltages. This is testing with my Corsair 650W PSU from ca. 2008. The only problems here are a weak 12v rail, a weak 3.3v rail, and -10v on both the -5 And -12v rails. I've attatched an image of what HWInfo spits out when the system is under load by Prime 95.

Don't worry about what it says the vcore voltage is, the program itself shows ~1.2v under load in the CPU voltage specific section, the exact same numbers it showed before all of this happened.

These voltages do not appear incorrect (at least, in the same way these do) on the 2008 system or the PSU tester.

[EDIT]

These are the voltages that HWInfo is giving me at idle:

And the voltages SpeedFan gives me at idle:

And these are the voltages that HWMonitor gives me at idle:

These were opened sequentially, but I captured these images within roughly 30 seconds to a minute of each other. If I were experiencing voltage swings that severe, I don't think I'd be typing this out on the very computer I've been discussing right now.

I tested it under Prime 95 load for about 2 hours and 20 minutes, and the CPU voltages didn't get out of spec (1.2v, occasional spikes to 1.3v and sometimes 1.4v, but it was doing this kinda stuff before all of this happened anyways), but the temperatures still reach upwards of 83c (The problem that caused this whole debacle in the first place when I decided to install a front panel fan and see if I could avoid buying a new cooler, hmph). I've gotten a Wraith Spire MAX in the hopes of reducing CPU temps.

I think the VRM hasn't been toasted, knock on wood. I'm still a little apprehensive about the safety of other voltages- I've went ahead and got an EVGA 500BQ, as I've had a very good experience with them overall. I've had an EVGA 450BT for over two years that has run both a Core2Quad Q6600 + Radeon HD6770 system, a Core i5 2310 + Radeon HD6770 system, and a Core i5 2310 + GTX 1050Ti based system (GPU upgrade). It's ran that last configuration for what's likely been over a year. I remember when I first got it because a dodgy 500W PSU that had a 6-pin connector died. I was playing Garry's Mod of all things, I smelt a very strong scent of ozone, turned my PC off, and it wouldn't turn back on. This was before I knew nearly as much as I do now, and so I had no comprehension of voltage readings, "bad VRMs", or bad individual components. If it turned on, as far as I was concerned, it worked. I asked my mom for a new PSU in a panic, and she got that and I was able to hook it up and see if it worked with the EVGA PSU.

The PC and everything in it was okay.