MiamieNeSex,
Sorry to disappoint you, but there is no magic way to pull out the CCU. You must take out the clock, the vents, the lighter, the console box, and the trim that goes over the CCU and radio. See the Service Manual. Hint: Pry down the chrome ring at the top of the shifter skirt, and unscrew the shift knob before pulling out the console trim.
As for the lights in the CCU display: Does every function of the CCU work otherwise? If so, then it may well be confined to the lamps, display unit, or display driver circuitry. There is a connection to the Dash Brightness Controller, so there may be lamps inside, but this could be just a level to the circuit board to tell the CCU how bright to make the display, whatever its nature. You will just have to take it apart to find out, unless someone else on this forum has been there.
Good luck,
Bill