Like bender said....if there is power to the compressor the clutch should engage unless the air gap is to wide so that the magnet can't pull it closed, it's burnt up or no ground.
Try lighting a small automotive bulb with the wire supplying the compressor......i have seen cases where the wire will show 12 volts but there was a weak connection somewhere so that the wire couldn't cary enough amps to operate the clutch....could also just run a quick jumper wire from the battery to the compressor to test this....