Just to let whoever is interested know, I think I figured out the problem.
I found a loose screw underneath the motherboard.  I guess what probably
happened was that whenever I would bump the case or put in a floppy, it
would provide just enough contact between the screw, the case, and the
motherboard to short it out.  All is well after taking everything out and
putting it all back in.

Thanks,

Lucas Taylor
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summary of previous post:
> New FIC PA2012 motherboard, ATX case.  Whenever I would insert a floppy
disk, or bump the case, the power would cut out.  I had to disconnect the
power from the motherboard and reconnect it for the machine to power on
again.  Also, it sometimes just wouldn't power up at all.