Chosen Solution
My iPhone 5 has been used as a music device for a while and was working fine, but the battery has swelled and split the case. I can find the new battery no problem and I’ve replaced them before, but the pressure from the swelled battery has damaged the pair of tiny rails that attach to the screen and affix the screen assembly to the back of the case. I can’t seem to find these rails anywhere. They are affixed to the screen assembly by small screws. Where can I get them?
Those rails are embedded in the screen, you can’t replace them without replacing the screen (or refurbishing the screen). If you don’t want to invest any more money in this device, I would just re-assemble it as-is. It may float a bit in the mid-section but it should be usable. Otherwise, you’ll need to replace the screen.
The “rails” that you are talking about are part of a new screen. Buy a new screen and you will have new rails.
The backplate on the LCD you need to transfer over and yours will be bent—iron it out and see if you can make it work, if not, then just leave it off—this is an iPhone 5.