Ok, I'm back. My A/C tech came by this afternoon. After trying to run the unit on the generator he thought maybe the digital stat was shutting down due to the power load so we bypassed the stat to no avail. It seems the unit is really not even trying to start. We hear a relay click but that's all. The generator doesn't draw down and the compressor doesn't even try to start. It's like there is a relay or something that shuts everything down before the compressor starts.
But it still works fine on shore power. And when I say shore power, it's plugged into a 100' Extention cord from my garage that's on a 15 amp breaker. We did check the generator by run a circular saw and a small air compressor. It did run the saw but not the air compressor. The start up amps on the saw was 10.5 amps and the compressor was 30 amps.
I'm still thinking about taking the generator back and getting a replacement just to rule that out.