That's usually a wiring problem with the Crutchfield harness, specifically the RCA connections.
Double check that the front and rear RCA's are plugged into the right spots on the back of the new head unit.
I think the GM factory wiring splits the speaker signals differently than a lot of aftermarket harnesses, so if you mix up the front or rear, you'll only get sound from a couple of speakers.
Also make sure none of the speaker wires got loose in the door panels. That's a common mistake.
If the RCA's are solid and you still have no sound from some speakers, you might have a bad wire in the harness itself.
The Crutchfield kits are usually good, but it happens.
After that, my next resort would be to contact Crutchfield's tech support and consult for a diagnostic check.