One problem related to power train has been reported for the 1999 Buick Century. The most recently reported issues are listed below.
I pulled into a parking space on a slight incline and was just releasing the brake pedal to move forward when the car lunged violently forward as if the gas pedal was to the floor. There was not enough time to do any thing expect a reflex to turn the wheel to avoid hitting the building head-on. The car scraped the side of the building only stopping when it hit a van. After the car stopped moving, I put it in park and turned off the iginition. The impact was not strong enough to deploy the air bags. My feet were not on the brake or gas when this occurred. My son-in-law went to your site to see if there was a record of this happening before and there was almost an exact description on a previous incident.