Florida state is not even close to the right answer. Their last undrafted year was 1983.
The longest streak I could find at nfl.com is USC. They've had someone drafted every year since 1947. Second place was Notre Dame, since 1956.
Lehigh and Lafeyette
34 - Northwestern 1979-1982
Kentucky wildcats
Mickey Mantle's longest hitting streak was 16 games.
Their longest is 8
UCLA's 88 game win streak is the longest in mens basketball
baylor
Columbia lions
Lehigh and Lafeyette
womens college basketball. uconn
Kansas State
Miami
the longest win streak in Division 1 College Football history is: Oklahoma - 47 wins - 1953-1957.
bates college
As of Apr 18, 2013, Bryant University has the longest Division I Baseball winning streak, which is 19.
south carolina
Iowa