I don?t have electrical diagram of Carrier Tech200ss with me. It sound like the compressor is trying to start and it not getting enough power. You said you check the capacitor for the compressor and it ok.
You could check the voltage in the contact to make sure it supplying the correct amount. We know the contactor is providing power to the condenser fan. Check the ?little black on one of the terminals? to make sure it not bad.
Yes, it possible the piston is stuck. What is the serial and model number of your central air conditioner units? I?ll try to find electrical diagram for it.