That l.e.d. is the status indicator for your onstar system. It should be green when all systems are normal, and only turns red when the onstar controller has detected a system fault. That also means that it set a diagnostic trouble code (dtc), and anyone with Tech2 scan tool can retrieve it.
Simple check: I am not sure what year your TB is, but if your On-Star antenna is located on the side glass, go to it and see if either the antenna is loose or broken. Unscrew the antenna and check for corrosion. Also, check to see if the antenna cable has come loose.
