its a common pontiac problem. ive had 4 pontiacs with 3 of them being grand prix's and all of them had that problem. Check the article or link below for more info of common probs. the auto defogger is #1

http://auto.consumerguide.com/Auto/Used/reviews/full/index.cfm/id/2610/act/usedcarreviewreliability/

2004-06 Pontiac Grand Prix: Reliability
Trouble Spots
Consumer Guide's® Auto Editors have scoured repair bulletins and questioned mechanics to search for commonly occurring problems for a particular vehicle. In some cases we also give possible manufacturer-suggested solutions. In many instances these trouble spots are Technical Service Bulletins posted by the manufacturer, however, we have our own expert looking at additional vehicle problems.

Audio system: Radio reception may be poor or have static because the rear window defogger may have invisible cracks in the grid lines. (2004-05)

Brakes: The front brakes may get noisy in stop-and-go traffic because a film develops on the brake rotor. Redesigned brake pads eliminate the problem by continually scraping the film away. (2005)

Electrical problem: The PCM was being replaced for a defective chip under a voluntary emissions recall because it affected the fuel pump and EGR system. (2005)

Electrical problem: If the OnStar system quits or won't come on (no power), but comes back to life if the fuse is removed for five minutes, the vehicle communications interface module must be replaced or else the problem will recur. (2005-06)

Fuel gauge: The engine may not start or may stall because the tank is empty yet the gauge shows fuel remaining, or the fuel gauge will not show full after refilling due to sulfur corrosion of the fuel level sender and if after treating with Fuel System Cleaner PLUS the problem remains, the sender may need to be replaced. (2004-06)

Fuel gauge: Noises from the rear of the car when there is about a quarter-tank or less of gas are due to the fuel pump pulling in air and there is a redesigned pump to fix this. (2005)

Transmission problems: Transmission (4T65-E) may lack reverse, may slip in reverse due to loose bolt in valve body, which must be retightened along with replacement of the channel plate gasket. (2003-04)

Water leak: Water may leak from the A-pillar (between windshield and door) due to a seam that was not properly sealed or onto the floor from the fresh air intake grille (2005) or the water deflector under the cowl needs to be replaced with an improved component. (2004-05)