Check the electric panel push the contactor by hand it runs the fan on the condencer but it will not stay on what can be the problem, the capacitor looks rusted but not bulget

If the fan and the compressor run when you manually close the contactor you either have a faulty contactor or faulty low voltage wiring to the contactor.

Check for voltage at the low voltage terminals of the contactor. If you have voltage replace the contactor. If you do not have voltage start looking for a break in low voltage wiring.