A compressor that turns on and off constantly, "short cycling" is a sign of a low refrigerant charge, a low charge will cause short cycling at any RPM.

A weak compressor could result in poor or no cooling at low RPM and OK cooling at higher RPM.

A weak clutch coil could be the problem.

A weak clutch relay can cause the problem.

A defective pressure switch could be the problem, it's easy to check, with engine running and A/C on, unplug it and use a jumper to connect the two leads, [yellow/white and blue/red

First thing I would check is the condenser fan, no airflow would result in high head pressure and poor cooling.