Find and fix the leak. From your description, you may have a LOT of work just as it is, and as said by kcconawa, it can only get worse. I don't have a lot of experience in tracking them down so I'll defer to the other experts here or RV.net on that.
As said by others, these fridges don't work like a home unit and are almost silent - actually completely silent when running on electric. Leave it on overnight and see if it gets cold. I believe they run better on propane than electric. Also, if yours can run on DC voltage because it can run down the batteries VERY fast in this mode. My Casita had a DC option which I tested when plugged in but never used. AC when available or propane only for me.
FYI they work by boiling ammonia. If there is any type of ammonia smell you are likely looking at needing a new cooling unit. Contact the manufacturer (either Dometic or Atwood).
Good luck and post your progress/questions!