Welcome back!
I had the exact same issue you're having with your car with my 97 T/A. The digital clock would go black and the radio and the windows wouldn't work when that would happen but if I'd give the dash a good whack near the radio/glove box area the digital clock would come back on and everything would work again. I tried for a long time to figure out what it was on my own but I seemed to be getting no where fast. So I talked to a friend of mine who is an ASE certified tech and one weekend him and I started "tearing into my car". While I turned the car on and off to get the problem to show up, he started to dig into the dash area. After what seemed like forever we got it down to the area by the glove box. With that we took the passenger side of the dash under the glove box apart and got to where the BCM (Body Control Module) is located and got the BCM out of its' holder under the glove box area. With me keeping an eye on the digital clock he started wiggling the wires that came out of the BCM. Lo and Behold. guess what we found - that if he'd wiggle two of the wires coming out of the BCM he could make the digital clock go on and off.

With that he popped the pigtail connector and we took the BCM out of my car after marking which two wires where causing the issue. We took the BCM over to his work bench area and we looked at his detail schematic of the BCM. We found that those two wires are the ones that supply power to the radio and the windows. Being curious as to what was going on we popped the over off of the BCM to see what was happening. What we found on closer inspection was that the two female parts of the pigtail connector that was on/in the BCM had slight cracks in them and whenever the male part of the connector moved it would cause the female parts to move enough that they didn't make contact with the board., thus causing no power to get to those two areas of the BCM but if you'd wiggle the wires, bash the dash or even hit a bump/rough part of the road right, the wires would move and there would be correct contact again.
To fix it I got a new BCM from a direct wholesale place, then made an appointment with my local dealer to have them install and program the new BCM for me. Since then I haven't had an issue with my radio or windows suddenly quitting on me.
I'm not sure how much a new BCM, install and program will cost you now since this happened to me several years ago and I'm sure the prices for everything are different now.
Also just to let you know, if you do need to get a new BCM - Don't take the old one out and put the new one in yourself thinking you can do that and then at your leisure go and have the new one programmed cause it won't work. Get the new BCM or have the dealer get it and then have the install and prgramming done all at once cause the BCM has what I call a "one shot start up". What that means is that once the new BCM is in the car you've got one shot at starting the car before it is programmed for your car and once you start the car it WON'T start up again until it is programmed for your car since everything inside your car - including the VATS - runs through it and a new BCM doesn't have a specific VATS programmed into it. I don't know why GM done this but I guess it was so someone (ie a thief) couldn't get a new BCM, slide the old programmed one out, slide the new one in and then use any old GM key to start the car, steal it then do the same thing with car after car.
But good luck and I hope the issue I was having is the same one you're having and I've been able to save you some time, trouble and hair pulling trying to figure it out.