Before you start touching anything or calling a tech., get a voltmeter and check the voltage. With AC units the current goes up as the voltage goes down. In warm/hot weather and everyone running AC units, the voltage is gonna go down. How much is dependent on how the place was wired and how far you are from a transformer and/or main distribution panel. It's a common issue in the summertime.
AC units have a momentary inrush current of 5-6 times the normal running current so if the voltage goes down and the current up, a breaker may not be able to hold long enough to allow the AC unit to start. Changing a breaker can be a waste of time and money.
Check the blades on the shore power cord. If they are pitted or dirty looking, clean them until bright and shiny. If they dirty & pitted, there will be resistance and contribute to voltage drop.
If the cause is low voltage, you can get an autoformer (Hughes for ex.) to boost the voltage. A hard start capacitor can also help which reduces the startup current. You can try shutting off everything in your TT and seeing if the AC will start. This can sometimes work if you are marginal.