I know that everyone must be dying to know the answer.
The last season where the Utes ended with an overall sub .500 record was 1903. That year the University of Utah had three wins verses the 12th infantry, Fort Douglas, and Ogden High School. Also according to the record books the University of Utah is 0-2 against the YMCA. I hate those guys!
As far as the TDS they had an overall losing record up until the end of the 1983 season.
And to add to your in state record knowledge Utah State is currently 4 games under .500 on their overall record with 513-520-28 (0.498)