|Looking at the photo of your keyboard it appears that the keyboard does have backlit functionality. See the opaque area below the keys? This isn't present on a standard non-backlit keyboard. |
Why it doesn't work is a mystery though.
I just read a thread that hinted at Fn + F9 to toggle the backlight on and off. Worth a try.
Also try shutting down the laptop completely, disconnect the power cable and remove the battery. Next hold down the power button for approximately 10 seconds. Reassemble the laptop and power it on.
Apparently while the laptop is powering up the keyboard should light up momentarily during the boot sequence. Keep an eye on it to see if it does.