It may be that the keys are just a sticky. I would remove the top case, pop all the keys off of the scissor assemblies, and thoroughly clean the scissor mechanisms, the rubber "boots", and the keycaps themselves. The area under the keyboard can get pretty sticky after several years of use. Also, if you find that cleaning doesn't resolve your issue, you don't need to buy a whole new top case. You can save money by buying a replacement keyboard, sometimes you can find one on ebay that doesn't have keycaps, those keyboards are even cheaper.

I think your best bet would be to buy a used Apple TV from ebay, and replace the parts into your Apple TV. Unfortunately, I don't think replacement parts are available. Best of luck!