If the belt slips: turn the engine off and turn it back on again, the a/c will work everytime.
If the ignition switch is bad: repeat the above test and the a/c may not be on everytime. But if you turn the ignition key left/right a little while the engine is running, you may get the a/c back on again.
I assume you check all the related fuses. Visual check of the fuses is not able to find hair line cracks or corroded contacts. You really need a test lamp or a volt meter.