Automatic Transfer Switch problem

My Ac will not run off generator. It runs fine off shore power. When trying to run off generator the AC will try to come on and then shut down to only fan working. Generator will still run, but produce no power and AC fan will run, but no compressor(just warm air)then later it will produce 120 volts again but, no ac compressor. Thought it might be automatic transfer switch so I wired a female plug end to the out put of the generator and plugged my shore power line in to it. AC and generator all runs fine. Do I need a new transfer switch?

Thanks
Mike