I realize this is an old post but Solas, did you figure it out?
I have an 06 Z71 and its doing the exact same thing. Warning lights pop up on dash, all gauges drop to zero, radio turns off, windows/doors wont work, etc but truck still runs. If I have AC on , fan will continue blowing but compressor not sending cold air. If i turn the truck off and restart, its usually fine.
Fairly new Interstate battery, will check ground and connections but this is driving me crazy