yamaha g100 1x12 version 3, amp issue - no sound (sometimes)

[phatt]

You have not mentioned that you soldered the failed joint?
SO,,,
If the solder joint was loose as you noted and you have NOT re-flowed that joint, then it only takes a bump and the amp will fail again.
To fix the issue you will need to remove the whole PCB to access the solder side and re-flow the failed solder pad. If you don't feel confident in doing the above then you will need to take it to a repair shop as it's a tricky job.
Phil.

[g1]

my question is, could a bad relay that doesnt engage cause the buildup of heat at the voltage regulator/resistor?

No, the heat is normal. Voltage is dumped at the resistor and regulator by converting it to heat.
More likely there is an issue if those parts do not get hot.

And all that heat shortens the capacitor lifespans.  So caps near hot spots like that often go bad before others in the unit that are not so close to heat sources.