I do a lot of refrigeration work as an advanced DIY guy. One of the things that I have learned is that some refrigeration and AC equipment is exceedingly bomb proof and can be revived even when everyone tells you it has to go. This is more true as the equipment gets older. Of course the replace/repair equation is easier for me because I di my own work and enjoy learning how things work as I fix them.
That said, sometimes its charge, start capacitor, even relatively cheap compressor/dryer, etc. I have revived many systems for under $100 when someone said a new system which can be $1k-$5k. Especially in your case where retrofitting is so painful the cost benefit equation changes. Do you know why it does not work properly? Here are some of the possibilites:
Start capacitor
Start relay
defrost heater
defrost board
main board
Evaporator fan
Compressor fan
Compressor
Leak
Many of these parts are low cost on eBay etc. I just fixed a 20 year old GE fridge that needed an obsolete defrost heater that I got on eBay for $15. Took longer to melt the ice block than fix the heater.
Let me know if I can help.
George