It's an interesting question. I'd probably put South Carolina and North Carolina as examples, though neither has quite funds A&M has. UNC has a lot of cash, but basketball will always get #1 billing. South Carolina has an incredibly rabid fan base dying to win big, but never has really threatened to win it all nor do they have A&M financial backing.
Saw Georgia Tech mentioned earlier, they probably are the reverse outlier. Top academic school, small enrollment size and small fan base. But yet has 4 National Championships, most recent in 1990. Even has 5 SEC football titles before they left to go independent in 1964 in what must be viewed as one the dumbest athletic decisions in the history of sports today (leaving the SEC). GT does not have the resources financially to compete with 10+ wins per year but usually has decent success 25% of seasons.
I am not sure Purdue really has ever had much national success in football and does not have A&M money.
Ultimately, the answer is probably no - schools with big fan bases, incredible financial resources, top facilities, and no major success the past 75 years.