I have no experience with the Warn Powerplant. Does the motor drive both the winch and compressor, one at a time, through some sort of transmission or shifting mechanism? Or is there a motor for the winch and a separate motor for the winch? If it's just one motor and it works OK for the compressor, you need to look at the "transmission" between them.
Edit: I just looked at the parts diagram. It looks like the compressor is between the motor and the winch. There is a "Mode" selector between them. Have you tried to work the mode selector back and forth to see if something is hung up? Does the selector seem to have full travel. I think your problem must have to do with the "Mode" selector. Perhaps it has some sort of power switching device to prevent it from running in-between modes or with both loads at the same time and that device or its contacts are burned and making poor contact in winch mode. You might see battery voltage at the motor terminals in winch mode, but have insufficient current to actually winch due to burned contacts. Warn has pretty good customer service. Calling them would be a good idea. Good luck.
Parts Diagram Link:
http://www.warn.com/truck/ReplacementParts/parts/249/73591A4.pdf