Keezer compressor issue

I made my keezer and adjusted the coarse adjustment screw on the stat per the thread on here. It worked fine for about 3 months, holding a steady 36-38 degrees. Then the other night I went to pull a pint, and nothing came out. Keezer was frozen! I unplugged it, let it warm back up to about 40 degrees (about a day and a half) and plugged it back in. It is holding the temp at 40, but when the compressor kicks on, it only runs for 15-20 seconds and then shuts off. About 5 minutes later it kicks on again for 15-20 seconds. Over and over. I know this can't be good for it. I checked the compressor compartment, and there are no obvious reasons - it is clean and everything is connected. The compressor is hot to the touch. No odors like anything burning up.

I bought the unit off Craigslist. A Kenmore 7.1 cuft. Appears to be no more than 5 years old. 4 kegs in it, at a various stages of fullness, so I think the thermal mass is good. I have a fan inside to circulate the air also. The only unusual thing that happened recently is that our power went out for a couple of hours, and I think it may have been the same day it froze up. Coincidence?

Any ideas? Would an external stat help? I really don't want to have to get a new freezer, make a new collar, etc. if I don't have to. TIA.

If you want to find out if you could use an external controller, set the thermostat well below freezing and see if it keeps running. Yes, you may have to remove the kegs until you know one way or the other what's going on...

Cheers!