'93 Civic EX
 

Bought the car almost three weeks ago. AC isn't working and hasn't been working since I attained the vehicle. When turned on it simply blows out hot air. I was going to apply the conversion kit to change it from a R12 to a R134, but was told to get it inspected first to make sure it doesn't have a leak somewhere. When I took it to the shop, the mechanic told me they couldn't test a R12 system. ...any suggestions as to what my next step should be?

R12 can be converted to R134. You do have to evacuate the old refrigerant and its best to do that at a shop that has the correct equipment. its not something you want to vent into the atmosphere. However, once converted to 134 then you can get the system tested and charged.

I've seen the R12 to R134 kit at AutoZone for like $45. I'm just concerned that if I covert the system (which is for the most part just adding an attachment to the posts and adding freon), that there may be a leak, and since the majority of the system will still be an R12 system (tubing/piping) that a repair shop won't be able to fix the leak, since they don't service R12 systems anymore.

Don't use the conversion kit, those cars will convert OK but you need to do it properly-- which means (at a minimum) find and repair any leaks, remove the compressor to change the oil, replace the receiver-drier, install good quality adapter fittings, evacuate fully, and charge.

There's a chance that it is still full of R-12 and the problem is something else. Unplug the pressure switch and check it for continuity. If the switch is closed, the compressor should run when you press the button.