Look where the seat cushion is attached, there should be a few13mm and 10mm nuts holding the seat pad on, with the seat pad removed you should be able to remove/replace the motor.
Can you look up under there and see the shaft coming from that motor?
If so and you don't want to replace it right away, you should be able to use a flex extension, and a small 1/4" ratchet, along with a 12mm socket used on the end of the motor shaft should let you manually adjust the seat, just unplug the motors electrical connector when doing so, or have somebody hold the switch to raise the seat as you manually raise it.
Attached should be an exploded diagram of that area, hopefully it helps a little.
If you want to replace that motor I'd check a few junk yards, or you can pay a bit more than you would used, and get it new from a GM parts seller...
2006 Pontiac Grand Prix GT with SC
1996 Buick Park Ave NA