Should I just tell them the circumstance surrounding not finishing or just decline the offer.

Tell them the circumstances. Maybe it will help, maybe not. You have nothing to lose in this situation.

The next time, just start with the truth and you won't have to feel terrible.

Not finishing school has always bothered me however I've always felt like I had a degree because I had got so far in my education.

Feeling like you had a degree and claiming that you have one aren't the same thing. After 12 years, it's perfectly reasonable to feel that you have the equivalent experience+studies. That's something you could call out in your cover letter or discuss proudly in your interview. But claiming a degree you haven't actually earned is improper.

Instead, just list the years you attended and don't claim the degree you haven't earned. If it comes up in the interview (and it probably will), then you can explain the circumstances that prevented you from completing your studies and actually attaining your degree.

And remember, it's never too late to complete a degree program. You might consider going nights and finally earning that degree. That kind of drive goes over well in an interview.