Hello Redford and Welcome to the Forum:
The 24v systme is there to make the contactor pull in. If the contactor is stuck, you may need a new one (take the old one with you). Also a stuck contactor means either a blown fuse or breaker, or the compressor is dead. Since the contactor is cheaper than a compressor, I would start with a new contactor, then make sure you have the high voltage and push the new contactor in to see if the compressor runs.
To test the compressor independently; disconnect all wires from the compressor, use an ohm meter, you will notice three spades sticking out from the compressor. Touch your ohm meter lead to one of the spades and the other lead to mechanical ground, record the reading. Now, repeat the process with the other two spades, writing down the reading on each one. If one of the readings is equal to the other two readings added together the compressor should be good. If that is not the case its time for a new compressor, and that means its also time to call the qualified repariman in because he has the equipment to remove the refrigerant ecologically.