I recently installed a DVD drive into my PC. (2 days ago.) Since then,
I get spontaneous power loss periodically - sometimes seconds after
booting, other times after hours of operation. I've tried replacing
the power supply, and I've tried removing all my hardware (other than
RAM), so I'm thinking it must be motherboard related.

Interestingly, trying to turn the machine back on does nothing.
HOWEVER...if I physically unplug the PC, and leave it off for a few
seconds, I then *can* reboot it. Looking inside the case, I notice a
green LED. When this goes out (after unplugging) it signals that I can
now successfully reboot. If I try to reboot before the light goes out
(about a 2 second wait) the reboot fails. I'm assuming the LED is
showing power remaining on the motherboard due to capacitors. I don't
know if that's a hint towards a solution?

Also, when I reboot, most (but not all) of the time the bios has been
reset as well.

Now the questions I've got a
1) Why? I've installed drives dozens of times, and never had anything
like this.
2) How do I fix it? Presumably a new motherboard will do the trick,
though I'd like to a) confirm that's the cause and b) fix the existing
MB, if at all possible. (Historically, every time I've tried to
replace a MB I've ended up having to replace the entire PC. Apparently
my skills don't lie in that direction!)

Is there any chance I can salvage this board? I have no idea if
replacing the onboard battery, flashing the bios, or any of these
arcane things will do anything to help, or if it's physically broken
and needs a part replaced? A electrician friend tells me he thinks a
capacitor may have gone, but looking at the MB, none of them appear to
be swollen or leaking.

thanks a lot! any advice is appreciated!