To answer this question we would need to know several things:
Assuming there was a valid contract with Dell, who were the parties to that contract? Was one of them an entity such as a corporation or an LLC, which you now own? When you bought the business, did you buy the shares of a corporation or LLC, or did you just buy the assets of the business?
If the business you bought has "legal personality," meaning it was a corporation or LLC that you took over when you bought it, and if that corporation or LLC was one of the parties to the contract with Dell, then you may be on the hook. But if the prior owner represented to you that the entity you bought had no debt, when in fact there were debts, the prior owner may be liable to you for the amount of the debt he failed to disclose.
If the prior owner's individual name is on the contract with Dell, well, it's not your problem.
If you dispute the debt, you should do so immediately, in writing.
There's probably more analysis that could be done, but I'll leave that for others.
Good luck. Don't take the above as legal advice since I'm not licensed in New Hampshire. If you need legal advice, please consult a New Hampshire lawyer.