FM-Pac and Panasonic FS-A1FX

Well do you think that there is any power on the edge connector when the machine is turned off?
It might be wise to ask someone who know a bit more about electronics to measure the voltages for you.
You could break your msx if you short circuit the wrong connections while measuring the voltages ...

While I was taking photos of the internal transformer, I discovered the two 25v blue capacitors just poop'd.
Anyway, I can replace the capacitors, soldering is no problem for me, but its the internal transformer I'm worried about. How can I check the transformer if it still working properly?

That's glue, not electrolyte.
I'm not getting +12v from Pin48.
Check if you have +12V on the 78L12. If you have it there then follow the path from it to the expansion connector.

Check if you are getting >12V on the "I" leg of the 78L12.

On that leg you should have ~17 volt (coming from the blue wire of the transformer), that's the unregulated voltage.
If the "1" you are getting stands for -value out of scale- then I suppose it's good, you are getting voltage into the 7812.