There are way too many variables to guess. Can you ID what burnt on the control? Look for the obvious burns or discolorations that would normally accompany a failed component.
A pic of the board front and rear out of the plastic housing might help.

Your guess that the original board may have been bad is a good idea.

I'd say first check for any continuity between ground and either side of the plug. You can do this at the plug itself to start with. Something is shorted to ground and your goal is to track that down. Start with the noise filter unplugged to begin as close to the plug as possible.

This stuff can be a nuisance, If nothing is obvious and you have a working board you can always install it and use the gfci outlet again. Leave everything unplugged from the board initially, then plug things in one by one until something trips the GFCI outlet. Wear shock proof gloves or unplug the machine prior to each new connection. Hopefully the board survives the GFCI trip. It would suck to burn a 2nd board. If it's for a customer you might explain the risk and let them make the call about potentially frying an expensive part.