Can I sell a non-OEM product under my brand name?

No, that is a relative of trademark infringement known as "reverse passing off". You cannot market someone else's product under YOUR brand without permission, just as you cannot market YOUR product under their brand without permission. It's a form of unfair competition.

You can, however, purchase their product on the open market and simply "resell" it under the original brand, offering whatever warranty and service contract you want to. Of course, there is nothing saying you will make any money buying at retail and competing with a manufacturer.

Those that say yes to this question, have no idea which way is up. Use common sense, no name brand company is going to cheapen the quality just to be sold at Wal Mart. Wal Mart can sell cheaper by sheer quanity. Also, those that keep the rhetoric about chinese goods, obviously haven't been looking at labels in other stores, as about all merchants today have their shelves full of Chinese crap, but at a higher price for the same product.

I wouldn't see why not. Just because someone else doesn't want to exploit a market doesn't mean that you can't.

Just be aware that you don't have the kind of cozzy relationship that other manufacturers have with their OEM suppliers (better prices, warranty protection, etc). But if you still think you can make money at it, go for it.