re: Longest streak of being bad in a sport

I'm not sure if "bad" is appropriate, but LSU men's basketball was nothing special between our first Final Four appearance in the early 1950s, until Pistol Pete came to Tigertown in the late 1960s - and Dale Brown right after that.

LSU baseball was never really a great program until Skip Bertman arrived in the mid 1980s.

LSU football only had one bad stretch between 1989 and 1994, but managed to win 27 games and 3 straight bowl games in 1995,96 and 97.
Prior to 1989, LSU was #12 all-time in number of NCAA victories, and 10th in bowl appearances (we are now 11th and 8th, respectively.)