Just because the compressor is hot doesn't mean it's running. Can you hear it running? From what you've said, I don't think it's running.
The small tube coming out of it going to the condenser should be too hot to touch if it is running. If it isn't running, take a look at the capacitors. If the one in a metal can shows ANY sign of bulging, replace it. If there's one in a black plastic container, examine it for signs of damage - they can overheat very quickly and spew wax around before busting the plastic case open. If there's something that says "easy start" on it, it may have failed. The easy start and start capacitor get the compressor turning, the run capacitor keeps it running and reduces the amps drawn by the compressor.
