2001 Cadillac Deville A/C compressor

There are several possibilities as to why the compressor may not come on, the least probable being the PCM. The compressor relay is grounded by the PCM, but it can inhibit operation due to certain faults, low ressure or a false indication of low pressure is one of them. Your first check should be the A/C CLU fuse, in the underhood fuse block. The compressor relay is in this fuse box as well, a quick check for a failed relay would be to swap it with another relay of the same type(you should have several in that fuse box). If the relay is not the problem, then the next thing would be to check trouble codes. There may be a code/fault that is set prohibiting compressor operation, and you could have no visual indication. To check for codes, press info up, and the on/off buttons together until after the segment check, and then the info display will read ALL, if you press on/off again it will read ALL CODES, and if you press it again it will start displaying codes. The codes we are concerned with are ACM or DIM, and PCM codes. Record the codes that are present, and report them. When the system was recovered for service, how much refrigerant was removed, and how much was replaced? If the system sees ow pressure, it will prohibit compressor operation