A/C not blowing cold air

I have the Denali model with rear air. I noticed air was not cool when the A/C is on. The A/C compressor engages for about 20 seconds then cycles off. This cycle repeats whenever the A/C is turned on. The air never gets cool. I used a charge kit and added R-134a until the guage indicated the appropriate pressure. The system only needed about half of the refrigerant in the can. I do not think the compressor is engaged long enough to cool. The pressure remains constant so I do not think it is a leak or insufficient refrigerant.

I have a 2000 yukon 4x4 and need to replace my A/C compressor. My question is do I need to also replace the condensor and completely flush the system. And can the exsisting condensor, oil and freon by reused.

There are no leaks that I know of I am looking at replacing the A/C compressor becuase the belt tensioner bounces loudly when AC is on and while accellorating. I have already realced the belt tensinor and belt and the noise it still there. It stills blows out cold air in the fornt and and not so cold in the back of the yukon.

1. A/C belt broke (replaced).
2. Tension-er broke (replaced).
3. A/C belt broke (replaced). Just prior to break, heard a rattling noise. Before replacing belt I checked the pulley and clutch. Both seemed to be free and no apparent drag.
4. Heard a rattling sound, but the A/C was not turned on and the belt broke again. The pulley still turns free and there is no indication it is the bearing and the clutch seems to rotate fine too.

I know if I have to replace the compressor I will have to pull a vacuum. If its a clutch problem and I remove the compressor to replace the clutch will I need to pull a vacuum when I replace it or will it hold its pressure with the manifold removed.

Please help.

AC is blowing out pieces of filter. Where is the filter located?