Yeah, any product they sold in the past will be in their files. I'd think they could fix it, or far more likely, give you a store credit. Normally I wouldn't consider buying online and presenting the product to a B&M dealer for service, but this may be a unique case- if WalMart is the only authorized dealer, you may have to. However, don't be surprised if it originally sold for $49 at WM. You probably overpaid for the item.
This should serve as a warning to all prospective Ebay shoppers. You really do have to do some research before buying. "Lennox"? I've never heard of them before. You're wise to stick to established brands from reputable manufactureres, and it's a good idea to check with the warrenty info in advance.
Ebay has some good deals, but it's notoriously cluttered with junk from drop shippers and people trying to unload their crap on the unwary. If you check right now, you'll probably find a dozen guys trying to sell their drop-shipped Coby portables for $120.

WalMart sold thousands of the exact same model for $60. Those sellers are just praying that the bidder doesn't know about electronics and didn't do their homework.
The long and the short- try WalMart first. If they won't fix it or give you credit, you'll just have to chalk it up to experience and learn from it. Unless you just financially aren't able to buy a new machine, rest assured that you can get a really decent one for $50 or less. You can get an excellent theater DVD player for $125 at a B&M dealer and get good warrenty service. Crutchfield is a solid & reliable online vendor with superb customer support.
Best of luck to you.