We actually beat North Carolina that year (2001) in the 2nd round. Easily the biggest win in our history. Which kind of indicates the level of apathy for men's hoops.
To answer your question, though: 8 years ago, I think. Talor Battle was our best player, Ed DeChellis was still coach. We lost in the first round to Temple - doing this off memory, so fact checking required if anyone cares enough.
A good team has to have players capable of making plays...oh, wait - we're so there!