2001: Chris Weinke, Carolina Panthers
At Florida State University, quarterback Chris Weinke led the Seminoles to back-to-back appearances in the National Championship game (winning the first of those two), and swept the majority of the postseason awards in 2000, including the Heisman Trophy. Of course, the caveat to all of that was that he was 28 years old when all that happened, having spent a number of years playing professional baseball.
So when the Carolina Panthers drafted Weinke in the 2000 NFL Draft, they thought they were getting a mature rookie who could step in and play right away. Clearly, they were wrong. As a rookie in 2001, Weinke averaged less than 200 yards passing per game, threw 11 touchdowns, and 19 interceptions in 15 games.
After his miserable rookie season, Weinke was replaced by 36-year-old veteran Rodney Peete. Weinke hung around as a backup for a few years, and was out of the NFL after five seasons and only 20 starts.