The correct answer is 1997. In Lon Kruger's second season, the Illini lost both exhibition games before surprising everyone by winning the B1G (tied for 1st) with a 13-3 record. That was arguably the most surprising/overachieving team in school's history: Heldman, Turned, Hester, Johnson, and Gee, etc.
Back then exhibitions were a little different, mostly against a collection of foreign teams (often branded as "National Teams", although most were not) and traveling teams of ex-college players put together for exhibition games purposes (e.g., Athletes in Action, NBC Thunder, etc.).
The Illini got crushed by 26, losing to a team from Australia ("Australian National Team") by the score of 87-61, and then lost their second exhibition game to NBC Thunder 86-83. The same NBC Thunder team had lost to Eastern Illinois by 14 points in an earlier exhibition game. The Illini looked terrible in both games, yet they surprised everyone the rest of the season and won the B1G.