If the air conditioner is empty of refrigerant this may be why the compressor does not run. There is a low pressure cutout switch in the lines from the evaporator. Remove the plug from this switch and place a jumper wire across it for a just couple of seconds to see if this is why the compressor does not run. If compressor runs with the jumper across the plug then recharge the system. If not then you have something else wrong. If the compressor does run, fit a can of R134A with an appropriate hose (can, tapper, hose, and gauge can be bought in a kit) to the low pressure fitting. Tap the can to let the R134A flow in. In my case with the system empty the refrigerant flowed sufficiently through the system to build a little pressure and then the compressor started by itself. Some people said they had to jumper the plug for a few seconds to get the process started, but I did not.

If the system is empty it may have a slow or a serious leak. I used the duPont "Suva" brand of R134A which has a dye in it. You can find a leak with a blacklight. The dye is very bright under the light - if you do this in the evening you would not miss a leak. However the evaporator is often the source of the leak according to many people's posts. That is hard to deal with because it is buried in the heating plenum. You would probably have to remove the heater fan to get close enough to see if that is the leak source. If so replacing it is a big job. With a slow leak you might be able to just recharge from time to time.