It happens to any device, not just Trezor so the USB cable might be the issue but since he bought Trezor last 2015 there is a possibility it's a hardware issue it could be the USB connector or shorted parts like capacitor or ICs.

Here's a sample of the Trezor board.



I just want to help 1GUARDIAN(And also others) if he doesn't want to buy new.

First thing, check the USB connector it might have full of dirt and rust to remove them use a brush and lacquer thinner(Or any rust cleaner, alcohol, or fluid) then test it again.

If not, you must disassemble the Trezor as shown in the image above then do this clean the ICs with brush and thinner make sure LCD is far and protected.

If it still not doesn't work it might shorted capacitor or maybe one of the IC pins has lost contact with the board so you might need to resolder the pins to fix the issue.