The smart thing to do would be to pay off the debt first, but I could see someone preferring to start the business first. If you can work around the fact that you're in debt, meaning no outstanding balances or someone is about to sue and put you in jail type debt, then I would start the business first. You have to understand that business loans and financing for business equipment is pretty much off the table, but everyone has a computer and a cell phone these days. That could work starting out.
You'll never know, in cases like yours, when you'll come across money like this again(or maybe you will, but you'll have to spend it on something else). Many business savvy people would start the business, then worry about the debt later (or when they start demanding their money back) (cough***white people***cough).