The system will come on and go off while using the AC, supposed to do that. But, if it does it in quick succession, on, off, on, off...that's short cycling. Usually a sign of not enough freon. These systems do not hold much, so getting in the correct amount is very important.You need to start from scratch....
make sure everything is flushed. You may not be able to fluch the condensor, most newer models you cannot. If the clutch is all that was bad, everything should work like it did. Make sure you are getting power to the clutch. What are the pressures? Low side should be around 30psi, high side (depending on ambient temp) around 150-200.
But, you gotta get all the air out by evacuating the system. You probably need to take it to a shop that has the correct AC equipment. Hope this helps! Jeff