University of Miami,Florida. 58 consecutive wins,an NCAA Record
The University of Oklahoma
Northwestern wildcats - 30 1980
University of Colorado
UCLA with 13!
Linfield College in McMinnville, OR. 54 consecutive winning seasons as both NAIA and NCAA Division III teams.
UCLA has won the most consecutive NCAA Division I Men's basketball championships, but Kenyon Univ has the most consecutive championships in any sport with 30 in DIII Swimming and Diving. Hobart College has the most consecutive team championships in any sport with 12 in D III Lacrosse.
The Mount Union Purple Raiders have 55 consecutive victories, the most of any division of NCAA football. But they were not in "consecutive weeks". In addition to having one or more "bye weeks" during the regular season, there is a 8-9-month period between seasons to break up the "consecutive weeks". In fact, if you keep this "consecutive weeks" as part of the question, it's going to be very difficult for anyone to answer this question, and I don't see why the answer would be meaningful to anyone.
Florida with 34
No they do not have an NCAA football team. However, the US Naval Academy does have an NCAA football team. And the academy graduates both Navy and Marine officers.
Princeton, with 28.
Dora the Explora's