Whether or not a customer could make out a good case for getting past the liability shield of the limited liability company in order to make a claim against you personally would depend on a range of factors, including how you handled the business, contract language, advertising, how you handled finances, etc. If we assume you operated correctly, liability for any warranty should be limited to the assets of the company and not extend to a personal judgment against you. There are also statutory options for you to formally wind up the LLC that can give you a more certain time line in which potential claimants and creditors must file claims against the LLC or lose the right to make a claim.
Mr. Burville is, as usual, correct.
The threshold question that I ask with business/owner liability issues is whether the business has assets the owner is seeking to protect or whether it has no assets, and it is the owner's personal assets that the owner is seeking to protect. Your situation sounds like the latter.
I'd be willing to bet, although I hope I'm wrong, that this business was operated as a sole proprietorship (also known as an assumed name or d/b/a), rather than an LLC or business corporation under chapter 302A of the Minnesota Statutes. If so, there is no corporate liability shield, and you have personal exposure. Nevertheless, even with proper incorporation and adherence to the corporate form (I'm ignoring partnerships for the moment), which avails the owners of the "corporate veil," there is still have personal liability as to taxes. And you may have personal guarantees you executed with a lender, or collateral you pledged as security for a loan. Those are still enforceable (that's the point, after all). In addition, you may have signed a contract in your individual capacity rather than as an officer of the corporation. And, if this is a single-member LLC, please remember that single-member LLCs in some states are not able to shield the owner from personal liability. Though this is not the situation per se under current law in Minnesota, the Minnesota Court of Appeals pierced the corporate veil of a single-member LLC in a 2011 case.
I would also alert you to the Minnesota Contractor Recovery Fund. "The Contractor Recovery Fund compensates owners or lessees of residential property in Minnesota who have suffered an actual and direct out-of-pocket loss due to a licensed contractor's fraudulent, deceptive or dishonest practices, conversion of funds or failure of performance." See http://www.doli.state.mn.us/ccld/RBCRecovery.asp. It almost certainly doesn't apply to you. It only applies when a "residential contractor was licensed and performing any of the special skills enumerated under Minn. Stat. § 326B.802, subdivision 15."