Just add my 2 cents here.
My 99 GCL had exactly the same problem. A reputable mechanic checked the car for about two months and was unable to identify the problem. He recommended me to go to the dealer.
The dealer tested the different electrical units such as BCM, ECU, etc. They could not tell me where it went wrong but thought the instrument cluster might cause all the problems, including the power windows. They had the instrument cluster replaced. So far so good.