A cause of the air conditioner not working could be a blown fuse . To find out, do a continuity test through a multimeter ( you can buy it here ), and if there is a beep from it, the fuses are fine. If not, you just have to buy new fuses for replacement.
Problems with the starting capacitor
Check for any problems with the starting capacitor. To realize this, listen carefully to the engine: in case of problems, you should hear an intermittent noise. Using the multimeter will take away any doubts about its breakage or not. The resolution obviously consists in replacing the broken piece, buying a spare one.
Before doing this, make sure that the starting capacitor is not simply dirty. In this case, lift the air conditioner cover, clean it, remove any debris and wipe with a cloth soaked in white vinegar.
Exhaust gas or refrigerant leak
If you have an air conditioner that starts normally but does not cool or heat the air, the problem would be in the exhaust gas or in a refrigerant leak. Noticing the latter is not difficult, as you just need to pay attention and see if mold spots appear on the wall. Often the two problems coexist, and in both cases the do-it-yourself is not very prudent.