Valve stems...do the go bad?

Yes....it wasn't clearly stated that the OP had metal stems, but if you read his entire post, it was pretty obvious. In my younger days, I mounted tires for a living. Metal stems don't go bad unless they're struck by a hard object but the rubber slide on seal at their base does over time. I would replace the rubber seals and then check carefully with soapy water after the new tires are installed. They use a nut and washer and often are over tightened by Gorilla employees or under tightened. Typically when most tire stores change tires, the valve core is removed and thrown into a pile with others and then reused later. Most stores wont stock just cores. If you want new cores, they'll probably have to be removed from a new rubber stem.