On Ford's there is also a relay to power up the compressor, it is the same size relay for the fuel pumps and fan motor. One of my neighbors Winnebago on F53 chassis had the same issue and I loaned him my spare relay that I keep in my truck and it got his compressor back going.
Check your chassis manual, the box that the relays are in will be accessible on the driver's side either under the hood or under the dash.
The replacement relays can be bought from Ford or from any auto parts store and are less than 10 bucks each. These relays are a black plastic cube about one square inch in size and have 4 or 5 blade pins that engage the fuse panel.
Chris & Dianne
Jayco Designer 3110 SOLD 6-11-2016, looking for the next one.
F250 PSD 4x4 Crew Cab