You could get a separate, backlit keyboard for your computer, there's a bewildering variety of them on Amazon or newegg.com, starting at about twenty buck and going up from there. You can even get them wireless, you stick a little nub into one of the USB ports and the keyboard communicates via that.
Or, if you're using a laptop, get a little gooseneck LED lamp that (again) plugs into one of your USB ports for power, and bend it around to softly light up your keyboard without flooding the entire room with a bigger light.