I had a very similar problem on my Aurora too. It ended up being a loose connection on the dashboard. not only does the radio not ahve any wireing, the dash, climate control, etc also have the ribbon cables. If the connection comes loose to any of these components very odd things will happen. You'll need to take your dash apart and make sure all connections are tight. On my aurora the gauges would act erratic. I'd loose certain gauges at times (they'd fall down to a zero reading) and the DIC would display -----------------, and the radio would lose its time setting. I think your climate control module might be the module with the loose connection however.
instrument panel ribbon cable (the other end of the panel has a matching ribbon cable.)
dash with DIC removed, radio, and climate control. all are controlled by the ribbon cables.