Rubber insides and circuit transparent sheets of USB keyboard don't work outside of plastic case
There is usually a clamp to ensure even and firm pressure between the flexible circuit boards (the keyboard matrix) and the keyboard controller PCB edge connector. Just placing them on top of each other is unlikely to work.

You can see some details on a project I did using a keyboard and some footswitches in Soldering on keyboard controller circuit board. I use it for advancing video slide presentations with my feet.