I've got a 2003 C5 50th. My electric shock system does not turn on occassionally. This has been going on for about 2 months. About 2 weeks ago, the drivers seat started to hum when the key was pulled out. After manually moving the seat the noise stops. I checked for codes and came up with U1255H, U1064H, U1016H AND U1096H after LDCM and RDCM.

Any ideas to correct these problems?

I think you have a pinched wire. Under the seat is one place I'd look. Under the console is where the wires for the adjustable suspension are. They are very thin an easily fray. Does the fuel door open without fail? Another place is the accordian like sleeve between the doors and the A pillar. Pull it back to reveal the wiring. Any frayed pinched wires? U codes are loss of communications.
Check all of your fuses under the kick panel and under the hood. How is the battery? Funny things happen if the battery gets weak. There is a grounding point at the bottom of the A pillar under the moulding I'd look at those too.
This is a tough one with many potential causes. Unless you have extended warranty I would exhaust all efforts before going to a dealer. Post up all of your codes and symptoms at Corvettemechanics.com The best source for techincal solutions. Best of luck and Welcome to the coolest C5 forum on the planet

How do you know the shock system isn't turning on? Are there any other codes? The ones you posted are just for the doors. I would also check the wiring under the seat for a short.