1. A DIRTY filter will NEVER stop an AC from coming on.
2. I would replace the capacitor and see. That will cost less than $50. probably $20.
3. You CANNOT just report the problem to the ESC company. They will NOT give you any answer you want. What they will tell you is, Go to a Service Center, PAY for a diagnosis, then have the service center call the ESC with Part and Labor cost. Once it is determined it is a covered repair the ESC will issue a Auth number. If the bill is over $500, you pay $500 and the ESC covers the extra amount. If the bill is UNDER $500, you are on the hook for the Diag time(usually $150 to $200) then probably another $75 for a capacitor replacement plus part cost which will probably push the bill close to $400 to $450.
4. Odds are from your description you have a bad capacitor. Go up on top, remove the shroud, have someone start a Cool cycle while up on top. Give it 3 to 5 minutes. IF you do NOT hear the compressor start to hum a few seconds the capacitor is probably bad. IF you hear the compressor try to start(you will hear it) then it is possible the Compressor is locked up, BUT I would spend the few dollars and replace the Start capacitor.
5. IF after the capacitor it does NOT start and you then hear the compressor hum when trying to start, then go to the service center and have them Diag the problem. DO NOT TELL THEM YOU HAVE DONE ANY WORK. IF the compressor is bad, RV AC unit compressors are never replaced, they do not even have them as a replacement part. You will get a new upper AC unit and THAT $500 will be well spent as a new AC with labor will be around $1000 to $1500.
6. BAD NEWS is this. IF you need a new upper unit, odds are they are out of stock due to Covid supply parts issues. So, it may be months before they can get a new unit. Doug