They won a 2014 BCS game but can’t compete for a NC? But we can because we could 17 years ago?
They won, and made it to, a 2014 BCS bowl as the conference champion of the American Athletic Conference (the Big East prior to that year), their first year in that conference, moving from Conference USA. That was also the last year for the BCS, and the only year UCF was in a conference that was part of the "upper echelon" of conferences, which used to be the "BCS conferences", ones that had an automatic bid to BCS games. With the move to the CFP, the AAC was relegated to a tier down, part of the Group of 5, and out of the top level Power 5 conferences.
I could also point out that UCF was ranked 15th in the final BCS rankings that year, meaning the only reason they made a BCS bowl was the automatic bid. Also, while the BCS rankings don't exactly correlate to the CFP rankings, 15th is nowhere close to making the playoffs, and making a BCS bowl that wasn't the national championship just meant you were in a very good bowl game, you had no chance at a national championship.
I will also point out that this year, even with an undefeated record and a win over another team ranked in the CFP, they sit at 15th, 11 spots out of a playoff spot, with only one or possibly two, games left before the final CFP ranking to determine who goes to the CFP. They would have to jump, as of right now, at least 3 undefeated Power 5 teams, and a number of other one loss Power 5 teams to get in, which is incredibly unlikely; and as long as they are in their current situation, it's probably not going to get any more likely.
So, to answer your question, the fact that UCF won a BCS game almost 4 years ago, and that Nebraska last won an NC 17 years ago; is completely irrelevant to the chances of either team possibly competing for one now. Nebraska is in a Power 5 conference, UCF is in a Group of 5 conference, it's as simple as that. None of this post was meant to bash UCF in anyway, just simply stating facts.
