Can a high school failure redeem themselves enough to attend a prestigious university?

Assuming you can prove yourself at community college, I think you'd stand a shot at BU. Harvard or MIT, though...why do you want to attend those schools? If it's just to prove yourself, then no; you're probably not getting in. There are very few (if any) transfer spots available at schools at that level, and they're going to go to students who not only stand out academically but can make a clear and compelling case that specific resources only that school can offer are going to make the difference between a decent career in their chosen field and an influential one. If you can do that and have some evidence to back you up (not just grades, but research or internships), then maybe you can beat the odds. Just know that they're very long ones, and it may not be worth it if you can in fact get what you need somewhere else.