Thanks for the help.  Replacing all the caps went much smoother than usual.  Probably b/c I'm used to replacing caps on motherboards with tiny traces everywhere.
I was even able to find the problem caps.  #'s 56,57,50, and 40 had all melted to the board.  I just could not see it without the PCB right in front of me.  I've seen many bad caps, but none that bursted like this, and in all the same manner.