[brcidd]

You answered your own question- you stated the system cycled on and off rapidly- with little or no cooling I'll assume- this means your original cycling switch is functional and doing its job and working as designed. You state the pressures are good- it is well known that you cannot judge system refrigerant amount by pressures- the ONLY way is to extract and weigh the refrigerant to know if your system is charged to specification.

Why you replaced the switch is beyond me....you need to assure your refrigerant charge amount is correct first- then diagnose from there. Chances are real good you are still undercharged- do you have a gage set on it to read static pressure? What is the suction pressure when you have it jumped out- If less than 20 psi, you can damage the thrust bearings in your compressor.

Also you failed to mention make and model of your vehicle- which helps in the diagnosis...