If you have a multimeter, I would try checking voltages while it's running. You can't trust what the BIOS health monitor says, sometimes they're ridiculously off. But if you have a known good PSU to try swapping, that's also a good idea.
Depending what's wrong, sometimes it can be a board level problem that causes bad voltages or ripple. You can't measure ripple with a multimeter but you can check the voltage at least.
I don't know about that board, but sometimes the 3.3v supply is regulated onboard rather than using the rail from the PSU. If the board has overvolting options for the chipset/RAM then it's definitely regulating it onboard.
Try replacing the CMOS battery, or check it's voltage while installed and under load.
Also try a live linux CD/DVD as Aideka mentioned. It's useful to see if a completely different software environment ends up with the same problem on the same hardware.
I suppose it might be informative to boot up a dedicated disk diagnostic tool like HDAT2. Maybe it would clarify if it's actually finding (apparently phantom) surface errors on the disks or it's having basic problems communicating with the drive controller. I'm not sure how that information would illuminate how to proceed though.
Interesting that the same error occurs no matter what drive controller you use, what drive you use, and what cable you use, but only with this motherboard. All I can think of is an uncertain board level problem or a power issue (either bad voltages or too much ripple).
Have you tried resetting the CMOS to defaults?
Have you verified that all jumpers are set correctly? Especially I wonder if there are any jumpers that affect clocks or voltages. I know you said it's not overclocked but I wonder if there's any chance the PCI bus is unintentionally overclocked, and maybe it was stable for a while but now isn't. I don't know about this board but some boards use jumpers to set the PCI/FSB ratio. Others use a fixed ratio depending what FSB is selected, and if it's not one of the standard FSB settings the ratios they use tend to be overly aggressive.
Some boards have both a FSB jumper and then a BIOS option to change it. Those can be tricky - on those I've typically seen the jumper actually dictates the PCI/FSB ratio so if the BIOS is set differently, unintended PCI overclocking can result.
Is that CPU an 800/100 or 800/133? If the latter, try knocking it down to 600/100 instead. And if you want to try an underclocking experiment, go down 66FSB (in between values may overclock the PCI bus).
This is a longshot, but when you attempt to install Win98 or 2k on a drive, have you tried telling Windows to do a *full* format? I have run into rare occasions where for some reason Windows couldn't install successfully unless I did that. Apparently there was something going on with the drive that the quick format option failed to address, but full format did.
Some of the things you've tried seem to nearly rule this out, but I'd be tempted to try it anyway.