Depends on what "no longer in business" means - did they merge with or sell to another company who assumed their obligations, including their warranty? If so, then that new buyer should be able to help you.
Did they file for bankruptcy? If so, then it's very unlikely that any successor would assume these obligations.
Check the warranty to see which state's law applies to the corporation and its warranty, then check the Scretary of State records to see thae status of the company. Or call the company back, since they apparently still have someome answering the phones, and get more information about any successors to the company.
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At the very least, please call the Ohio Attorney General's Consumer Section and make a complaint. The Ohio AG has attorneys and investigators dedicated to holding companies responsible under the Ohio Consumer Sales Practices Act. Occasionally the Ohio AG's Office will file suit against a company on behalf of consumers and will seek to recover a consumer's damages.
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I agree with Attorney Koslyn. A lot will depend on what "out of business" means. If the company has filed for bankruptcy protection, you are going to have a tough time of it.
You can check the Ohio corporate records, here, to see what they have on the business, if it was in fact a corporation: http://www2.sos.state.oh.us/pls/bsqry/f?p=100:1:1317646823058057
Depending on the circumstances, you *might* be able to file an action against the owners of the business or the officers and directors, if it was a corporation.
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