There are several things that could cause the compressor to not engage.
1) loose wire. Make sure the compressor is actually plugged in.
2) Low freon. There is a pressure switch on the low side of the compressor. If the PSI gets too low, the compressor won't engage. Easy way to check is to hook up a pressure gauge to the low side service port. It is easy to add freon, but you need to find out why it is low and fix the leak (or not. I know people with very small leaks that just put in 1 can every summer).
3) Bad pressure switch. If the switch is broken, then it will act like there is no freon. On some cars, you can disconnect the harness from the switch and jump the 2 tabs on the harness. If the compressor starts, then you know the sensor is bad. Let someone that knows more about the C4 tell you this is what to do.
4) Electrical problem. I can't help on this one.
5) Bad clutch on the compressor. Replace.