[brucehart]

Your career is definitely not shot. I've known people who completely bailed on their first job out of college within a few weeks and bounced back on their feet almost immediately. I would contact the hiring manager (and maybe copy HR) and ask if you can defer your start date. Explain that you had some medical issues that prevented you from finishing your degree as expected. You don't have to provide a detailed explanation and they will likely not ask for one.

Say that you still want to work for them, but you are making up your remaining classes over the summer/fall and that you would be available to start at full capacity on X date. If you can start within a few months of your original date, they probably will be fine with that. If you can't start until next January or next spring, then they might tell you that it would depend on their needs at the time. Either way, I wouldn't leave school and then try to secretly get your degree on the side. Those kinds of decisions usually come back to bite people at some point in the future.