Good luck, but why should they? It would seem that they'd need more proof than just a sad letter from you - if that worked, everybody would write one.
It's not that your claim is bogus, it's that you had pretty much entered a contract, and contracts usually have pretty specific terms for release. (They're also often time related.) If I were somebody in the finance office, I'd want something else, like a doctor's letter corroborating your statement. But that's just me - maybe they'll be willing to negotiate .