The compressor may shut off due to tripping a built-in thermal (over-temperature) switch, or due to a "max-on-cycle" timer in the thermostat. Otherwise, if it never reaches the set temp, it keeps plowing on to get there.
Most refrigeration systems are very similarly built, what applies to one likely applies to most. So YouTube vids can still be a great resource for ideas where to look or how to fix.
Sometimes there's a schematic pasted or packaged somewhere in or near the compressor cavity, which may help in troubleshooting.
My bet at this point is loss of refrigerant somewhere.
In that light, here's a very recent thread on doing a refrigerant recharge:
https://www.homebrewtalk.com/threads/how-to-recharge-a-freezer-or-fridge.682877/It looks very doable, and affordable.
There are a few other refrigeration troubleshooting and fixing threads.
Moderator's Note:
I've moved this thread to the Kegerators & Keezers Forum, for better exposure on finding solutions to fix.
You can always
repost the request for a local DC area service in this forum at some point, as long as
discussion of your kegerator problem can be (mostly) kept to this thread.