I hope this helps. I'm also in Park Avenue Air Conditioner Hell. I've read books, talked to mechanics, been to the dealers. Here's what I can put together so far.
If you have different temperature from the driver and passenger sides, then that is a BLEND DOOR issue. The blend doors are little triangular devices with centers that rotate from an electrical signal. Their plastic gears can break, or the motor can lose the ability to move them. They are up under the dash but reachable from the cabin without removing much more than the black noise panel. (You may want to pull the glove box on the right, too). They are held in place by 3 screws (philips). They are on the driver and passenger sides, and each has a different letter (I've seen R and S labels on the ones in my car - may be an "L" as well, but I don't know for certain yet.) These fit in the palm of your hand, and are somewhat triangular. Look on ebay or web for this part number to see what one looks like: 89018383
At the center of the HVAC near the top, but reachable without removal, is a MODE DOOR. If you have an inability to get the air to blow anywhere but out the defroster, then that is a MODE DOOR issue. The mode door has a lever on the side, and you can move that manually. In my 97, the lever has no sense of any resistance to it. Evidently the doors have broken inside the AC unit. It's going to Buick soon - not looking forward to dealer pricing.
Meanwhile, we all see that lovely control head in the dashboard with numbers and fan speeds on it. That can also fail. Typically that loses brightness from what I'm finding. There are rebuild services on eBay. However, that is NOT the most significant control element. Instead, there is a PROGRAMMER (look up part 9353514 or part 16238774) that gives the bulk of the instructions. Mine had an IO error. This multi-box system means you may need a dealer to diagnose electronics failures. Dealers will charge about $600 for a programmer box. Junkyards are selling for about $40.
The 97 and newer have all electronic devices. The 96 and prior have vacuums. That distinction is rarely made in repair posts. The 96 and prior often have vacuum leak failures from the end points being dried out. DO NOT go looking for the vacuum system in your 97 or newer - they aren't there. (You'd evidently find a colorful array of hoses coming through the firewall if they were.)
If you do replace a mode or blend door or programmer or control head, know that you should turn OFF your HVAC and then turn on your car. Leave it sit in the on position for the car/off position for the AC for about 3 minutes. All the door positions will calibrate.
Folks, I sure hope that helps. I've spent waaaaaay too much time digging info on this issue. It's been quite a learning experience. Good luck - and if anyone knows a way to fix the MODE DOOR without paying Buick my first born, I'd welcome the insight. - Dave 97 Park Avenue