One problem related to brakes failed has been reported for the 1999 Buick Century. The most recently reported issues are listed below.
On Nov. 9th 2001, we were on our way to atlanta, the cruise control froze up at 70 miles per hour, I was unable to disengage it or turn it off and the brakes failed to respond , they were locked up also. Thinking that the accelerator might be stuck I tapped it lightly and the car sped up to 85 mph. I was in atlanta traffic and finally after about 5 miles I was able to get it to disengage. There was no place to pull off and I decided to turn it off. It instead reengaged and would not disengage for awhile. We finally got onto I-285 looking for a place to get off. As we got up to speed it once again reengaged and it took me nearly 8 miles to get it off again. This happened three more times, each time I was not able to exit. We were fortunate that we were able to get off at the exit to our daughters house and I unplugged it under the hood. I had no further problems. I have never been so scared in a car in my life. 85 mph in atlanta traffic & no brakes. I took the car to the local Chevrolet/Buick dealer (bennett Chevrolet/Buick) on Monday the 12th. They told me that the cruse control module had gone out. I thought that you might need to know about this potential for a fatal crash. We were lucky, please see that this happens to no one else, they might not be so lucky.