Now, the questions: what the hell happened?
Failures of tantalums (I've
witnessed) are usually due to reversed polarity: not only are these
particular parts long-term residents of the boards, but the unregulated +12V
supply is the highest DC voltage in the machine - how did the - terminal (DC
FWIW, I've just had tantalum capacitors explode for no good reason. In
once classic (!) case, I took an IBM CGA card from the box of PC bits and
plugged it into an expansion slot. One of the tants (a decoupling cap on
the 5V rail) exploded, but the board carried on working, the right image
came up on the monitor, and the machine passed the POST.
I'd just replace the caps and see what happens.
-tony