The Champ should chew through this load with no difficulty. Yes, you may need to monitor other loads, but the 3500/4000 has whopping surge capability and your AC isn't even in rotor lock yet.
I would not hesitate to call Champion tech support. They probably won't hand you a free replacement, but once you troubleshoot here, isolate extra loads, and if it still isn't working, then you should tell Champion. These simple units are designed to sit around for years until there's an emergency and then start on the first or second pull and perform perfectly.
Er, did you put oil in it?
