Keyboard backlight doesn't light

I have a Late 2011 MacBook Pro 15” which works fine except the keyboard backlight never lights up. Pressing the Fn-keys to make it brighter/darker will display (and change) the on-screen icon showing the current brightness level, so the Mac thinks it’s lit up, but the keyboard remains dark. I’ve reset SMC and PRAM, and even reseated the tiny keyboard backlight cable next to the fan on the motherboard, but none of that has helped.

Is this likely a motherboard problem, or is there anything else I can try?