http://engine-codes.com/p0530_chevrolet.html is the system charged properly? if not the hi pressure switch wont tell the compressor to come on.
as far as the pcm, if it comes out of the same year car with the same engine it should work, will likely need a security learn. thats easy and free tho.
the vin wont match, but that only matters if you have inspection. it can be changed with a tuner program. like DHP.