I'd make sure both terminals on the battery are bolted down tight first. One of my TGPs would randomly die at one point, and I eventually discovered it's because one of the terminals post bolts wasn't tightening down enough anymore. Changed the bolt, and never had a problem with it again. If that's OK, get the battery tested first to make sure it's even accepting a charge, or swap it with another batter if you have one handy just to test and see if it will take a jump. If the battery checks out, I'd check all the grounds as others have suggested. If any of these things aren't in good order, the jump box won't make a difference.
As far as getting to the back plugs, remove the dog bone motor mounts, and rock the motor forward a bit. Should give you more access to the back.