Check the tank for the compressor model 921.166360 that will not build pressure above 20 psi. If the tank is not leaking, look at the check valve to make sure that it is not restricted. If the check valve is okay and you have no leaks, then you would likely need to rebuild the compressor pump to fix this problem. You would at least need a piston kit (part E100251) and a gasket kit (part E100959). You may also need new valve plates (part E100228) and valve reeds (part E100229) if they are damaged. If you do not feel confident repairing this problem yourself, then you can have it repaired by a Sears technician. Here is a link that will provide the nearest drop-off locations:
Sears Home Services
On the second compressor (model 921.153101) that will not start, check the outlet that it is plugged into to make sure that it has power. Check the outlet power cord for damage. Check to see if it will start when the air tank is empty. If it will, then you likely have a bad check valve. If the compressor will not start even when the tank is empty then you could have a bad outlet cord, a failed switch or a bad motor.