[Fulltiming]

If these are Dometic basement airs, there are several potentials. The wiring could be corroded or burned in two. This would result in a complete failure of the air conditioner to start or if just corroded/loose connections, could cause the air conditioner to run at times and not at other times. If the compressor has given up, it could either never turn on thus no cold air, come on with a LOT of noise typically followed by tripping it a breaker or its internal thermal protection, or could have tripped the circuit breaker trying to draw too many amps. The third item is the condenser fan could be frozen. This could be a big problem because it is no longer available.

The description of 'one would not fire up', doesn't tell me enough to point you in the correct direction. It could be a momentary high draw that caused a weak circuit breaker to trip which would be easy and inexpensive to fix, to the compressor which would be several hundred dollars for the part plus labor to install and the cost of pumping a vacuum and recharging the refrigerant, to the rare fan which could require removal and trying to find someone to rebuild it.