Dometic A/C 13500 BTU Capacitor replacement

You can buy capacitors very inexpensively on Amazon and from other sources. I've replaced them on our HOME A/C (central system) so many times that I keep a spare on hand. Home unit uses only a combined HERM (compressor) and FAN RUN capacitor. No Start Device. The RV uses the same PLUS a Start Device made up of a Capacitor and a Relay. I keep a RUN cap plus a SUPCO SPP6E Start Device. So far, of course, RV hasn't needed one.
Not all Capacitors are equal. They are rated for various service lives in terms of operating hours. I had one of the cheap ones at the house and it didn't last long at all. That was when a parts person pointed out the difference and I got the better one.

Here is a link to info on hard start capacitors.
Air Conditioner Hard Start Capacitor
Not sure it is the answer to OP problem.

Luck you..I paid a lot more then that for an emergency repair in 100 degree weather I now carry a spare. Now I must say it was my wifes fault it burned up. She set the thermostat to the lowest setting before we left and 3 hours later it was frozen solid and putting so much strain it burned out the capacitor. I now carry a spare just in case. Only thing I'm worried about is replacing it myself I heard you have to de-energize the old one or something???? And always make sure you wipe up the fluid it eats anything. If any one knows how to replace one please post it!!!!! Thanks!!

One possibility, often times the blower shaft will corrode and seize during the winter here. If you try to start a seized motor too many times it will destroy the cap.

You may need a Hard Start Capacitor. Not sure this one is right for your AC. Dometic Duo Therm RV Air Conditioner Hard Start Capacitor