Altec Lansing ATP3 Speaker system transformer failed.

This speaker system I used on my main computer died yesterday - no power at all.
I traced the problem to the transformer, a 12.5V 2.5 A TP57U25F from Ten Pad Industrial. Testing the transformer coils, neither the 117V input or the 12.5 V secondary show conductivity - they are both open circuit. The fuse for the primary circuit was not blown.
My question here is, if both coils are open circuit, does this suggest that a major short on the PC board got the transformer too hot so it tripped temp circuit cutoffs in both coils, so it is unlikely that replacing or fixing the transformer will fix the speaker? Or, is this kind of failure common for such transformers?
If I wanted to try a different transformer to test the board, what should I want the transformers open circuit voltage to read on my Greenlee DM-20 DVM.  Should that be 12.5V? I do have a variable voltage variac I could use to adjust a slightly higher voltage transformer down to 12.5 or whatever should be needed.