I had the same problem with my '85 Delta 88, and I found out that the ECM had been bypassed, so in order to switch between heat and a/c, you had to open the hood of my car and manually turn a valve (Pain. In. The. ASS.) It turns out that the HVAC system that controlled the thermostat didn't have enough vacuum, so whoever the previous owner had working on her car obviously didn't know what they were doing, and took the easy route and bypassed the computer. May not be the case with you, but I'd look into the thermostat and HVAC system, especially if trouble codes don't come up. It might be something as simple as not having enough vacuum.
If it's mounted behind the glove box (as I assume it still is), if you turn on the air and adjust the temperature, there should be a little arm that moves to control the temp. Mine SLOWLY moved, and then didn't stay in place. If your little controller arm doesn't move promptly, the HVAC might not have enough vacuum.
At least this is what I remember from when we tore my a/c system apart last week.
But you don't mention whether the blower comes on at all, or if it's just the a/c that doesn't work (i.e.: The air doesn't get cold, but the blower runs - which was the case with me).
I hope this helps a bit.
EDIT:
http://en.allexperts.com/q/Oldsmobile-Buick-Repair-826/
This might help, too. You may be able to find answers here if you go to the bottom of the page, click on "All", and then press ctrl+F and search "a/c".
