Fast and easy OS X app, to copy and paste and store and retrieve, code and text back fast

Given that this is almost certainly not a hardware issue (there is, after all, no copy/paste chip that performs that function) and given the troubleshooting steps you have included, this still sounds like a task for your local Genius Bar. If it's a configuration issue or a software conflict, they can help you sort it out, and if it's a bug in OS X, they'll make Apple aware of it so it can be fixed.

As other answers have mentioned, you still have to isolate software as a cause by trying a new user or a new install of the OS (perhaps to an external drive).

I use FlyCut, you can do Cmd-Shift-V and then cycle through your recently copied texts with arrow keys.