Rick, when you say "kick the ground fault receptical," do you mean that as soon as you reset the GFI it immediately trips? If so, start by unplugging everything on the 120v outlets. Then reset the GFI. If it trips, the problem is in the wiring somewhere. Check each outlet, starting with that GFI. I'm guessing that you have it improperly wired, or one downstream from it is miswired. If all is fine until you plug something in, it is probably in that outlet. Start with the GFI and work downstream.
If all the connections at the outlets check out, it is possible that somehow a staple or nail has gotten into a wire. Good luck finding that! First disconnect ALL 120v power (including the inverter). Check each outlet to make sure that there is no power there. Then disconnect the downstream outlets from the GFI. That should be marked on the GFI, but sometimes it can be hard to read. Temporarily cap those wires (they won't be hot, but they can touch things they aren't supposed to), reconnect the 120v, and test the GFI again. If all works properly, disconnect the 120v, reconnect the downstream outlets, and go to the next one. Do the same thing. This time, though, there won't be any label to help you, so unless you can see where the wires are going, just pick one pair, disconnect and cap it (remember, you have a 50-50 chance of disconnecting the line from the GFI), reconnect power and test.
Chasing down electrical problems like this isn't terribly hard, just frustrating sometimes. A good meter, a helper with small, nimble fingers, a good light, and a sense of humor will get it done. Remember to make sure that 120v power is OFF.