Hi,
Yes the compressor might be bad. Or the capacitor. Because you can buy a 35 Mfd capacitor for about $20, you might as well replace it, and see if the compressor starts.
Of course if you know how to use a volt meter, you can ohm the compressor terminals from one terminal to ground (with the RV unplugged) and if you get resistance, then the compressor is bad, and you can not repair it.
Replacing the compressor is 'possible' however a 12,000 Btu compressor will run me around $400, and you are looking at about 6 - 8 hours labor, $40 in freon, $40 for a freon drier, and a 90 day maximum warranty on the replacement compressor. This is why they are called 'non-repairable' because a new unit with a 5 year compressor warranty is around $700 - $800 and sometimes places like Camping World will install them for a low cost (say a $5 installation sale special).
Good luck, and hopefully it will be a bad capacitor!
If you keep turning it on, then it will be a bad compressor very soon! I hope that you did not let it cycle on and off for more than a couple of minutes. It is very bad on the compressor (assuming that the capacitor was the only thing wrong with it to start with).
If the compressor is shorted to ground with say 100 ohms or less to ground, then it is really bad burnt up motor winding, and not worth trying to repair, even if you got a compressor for free. A low ohm short to ground is very acidic, and all that acid in the tubing will quickly start eating away the new compressor motor windings.
Fred.