By Jove, it worked! 🤣 I just tried one of the 2 "bad" boards again - the one that looks OK (with the new replacement caps), but would *not* boot up at all with a Palamino 1700+ CPU in it. With a Thoroughbred 1700+ CPU in it, I get no problems. And for the first time Prime95 doesn't instantly fail - it's running right ATM without any errors being reported.
I've gotta get myself some more of these T-breds. I wonder how high I can go with 'em?
Also: Speedfan says this t-bred 1700 is 63C. That's quite high. Perhaps it's because Prime95.exe was "cooking it"? Yes - I've stopped Prime95, and the CPU temp is rapidly decreasing...
Edit: I dug out that other second "bad" board. This is the one with distinctly rotten looking caps. I put a "simple" Duron in it, so as not to upset it too much, and proceeded to flash its BIOS with the "t-bred aware" BIOS. I then put the t-bred 1700 CPU in it, and it works, but only just. Prime95 fails every time, within about 20 seconds. SiSoftware Sandra sometimes locks up too. Games run OK though.
Edit 2: I seem to be having some success with the "rotten caps" board. Instead of increasing core volts in to this thing, I've done the opposite. Inside the BIOS, I *decreased* the core voltage by one notch setting. Now the board seems a bit more stable. I can run Prime95, and it doesn't fail instantly. The CPU also starts off cooler. I ran this test for several minutes, then got bored and stopped it. (But at least it didn't fail, although I realise this test needs to be run for ages.)
I guess the next step would be to get a low voltage CPU, such as a mobile t-bred. My guess is that it would help to stabalise a board which is unstable due to rotten caps. In any case, both "bad" boards have been spared their fateful journey to the recycle centre.