The radio will not turn off when you open the driver's side door ( have to open the passenger to get the radio to shut off )

Sounds like the splice problem in the driver's side door sill.

Some times water gets into the channel, and causes issues with the splices to the VSM ( Vehicle Security Module ). The big one seems to be the door input. Other symptoms can be the power seat ( if equipd ) does not work, or the power mirrors stop working.

On the std cab, the splice is closer to the a pillar, on the SuperCrew the splice is towards the c pillar where the wires route up the pillar.

The splice is a 3 wires splice ( 1 wire from 1 direction, to 2 wires the other direction ) that are covered in loom tape that looks like hockey stick tape.

Pictures of the splices.
std cab Blue w/ white stripe wire :


SuperCrew Purple wire


Be prepared with some 14 AWG wire to add to the splice ( need to cut back to find clean wire on both sides ), soldering iron for the splices, and marine heat shrink tube ( the ones with the water proofing gel in them ) to repair it.