Perhaps a backlit keyboard is too complicated. The simplest way to have a readable keyboard in the dark is to have black characters on a white background on each key. Having black characters on a white background maximizes the reflective surface area and makes it easier to distinguish each character versus having white characters on a black background. The light from the screen will illuminate the keys enough to be readable in the dark. I put stickers on my laptop keyboard which have large black characters on a white background. Even when the LCD screen is completely black on my laptop computer, enough light leaks out of the screen to illuminate the keys.