You say you "...can hear the compressor start up..."
Question: verify you hear the compressor start, or the fan/blower motor start?
In other words: are you feeling air being blown from the unit, but it's not cold or hot... or... is the air you're feeling cold and/or hot, but is not being blown from the unit with any force as it should?
I'm assuming that you've checked all of your circuit breakers...
I'm also assuming that, since you didn't mention it, you're getting no error codes on the thermostat.
The reason I ask is that my friend had a similar problem this past summer... where his unit would blow air, but not cold air. When the A/C would cycle on.... he heard both the blower fan & compressor start up, but then about 5 seconds later the compressor would click off. The fan would still blow, but there was no cold air. On his thermostat, he kept getting an E-6 Error Code on his thermostat for a faulty Humidity Sensor. In the end, he had to take it back to CW... where they replaced the sensor under warranty.
2013 VOLTAGE 3200 (EPIC I & II)
2014 Ford F-450 PLATINUM