Those all may be related, actually. The U2104 & U2105 are the ECU saying it is having trouble communicating on the CAN bus. The transmission is probably storing a similar code, and since it requires engine data to shift right, etc., it set the P0700.
There are 2 separate buses on the 2003. The GMLAN low-speed bus (which goes to the diagnostic port in the cab, stereo, door computers, etc.) and the proper CAN bus, which on the LB7 only goes from the engine computer to the transmission computer.
U2xxx codes appear to relate to the CAN bus, and U1xxx codes appear to be GMLAN, IIRC.
So, I would look at the condition of the wiring from the ECU to the TCM. There may be a pinched or loose wire.
A better scan tool would help to confirm what code(s) the TCM has.