'65 Continental,
If you want to do something by yourself before calling another tech (if the previous tech hasn't already done it), you can remove the freezer baskets (easy to do, you just need to roll them out and lift them up (you'll see there's a place where the rollers can go out of the tracks, one at a time). Then, you can remove the bottom tray and air duct to see the evaporator and condenser fan.
I have seen some that had melted during the defrost cycle, resulting in a melted fan (and plastic ducts). If you plug it once you see the evap, you at least could see what happens there when it runs! A Frigidaire serviceman once told me that the '63-'64 models were good ones. He didn't like the earlier ones with two blowers and a cold plate in the refrigerator section but there are still some working (and I plan getting a '62 soon!).
Unfortunately, what John told you is probably right but I still wouldn't give up too quickly if I were you. If you have space to keep it in a non-working condition until you find someone and the required parts to repair it, and if spending a few hundred bucks on it isn't an issue, you might get it going again! But first you have to find a tech that knows these! I like having things that are unique or unusual! I like old cars too and I like when they are unusual even if that means they are harder to repair or keep going! I take pride in having things that very few others have!
Some old car fans like updating their rides with easy to mod and easy to repair Chevy engines (including a few friends of mine who have hotrods). I don't!
Have you looked for traces of oil/refrigerant leaks at the compressor connections and service port?
Finally, there's probably at least another "member" on this board with a working '64 Frigidaire. It's a 14 cu-ft Deluxe with bottom freezer but it's very similar to ours. I don't know if he still has it but I'd like to hear from him about it!
see:
http://automaticwasher.org/cgi-bin/...NIMATIC1140.jpg&dir=/COLLECTIONS/UNIMATIC1140