The phone is locked to your carrier, and the carrier will normally have to unlock it before it can be used with a different carrier. They are extremely unlikely to unlock it if there is an outstanding balance on the account.
You could try a company like doctorSIM that unlocks phones, but the problem for you would be that because it was deactivated due to unpaid bills, it was almost certainly blacklisted. The different cellular providers share the blacklist specifically to prevent people from using phones they haven't paid for with the other carriers. If you think about it, they have a point. Today's smartphones can cost hundreds of dollars, and carriers basically spread that cost over the period of a two-year contract so that customers don't have to pay it all up front. If you breach the contract by not paying, the carrier doesn't recover the money that it essentially fronted you for the phone.