Since everything except inverter fed circuits are working (on generator), if I've understood the symptoms correctly, I'm gonna make a guess that your transfer switch is not working. You would have to check the voltage on the output side of the transfer switch with shore power connected and see if you have 115. I'm guessing you will not. If you check the same output side of the transfer switch with the generator running I'm guessing you will have 115. Not sure how being hooked up to a 15 amp circuit would cause that but it may have just been a coincidence.