As it turns out, this Inspiron 15 (3521) does not have a backlit keyboard available. Currently, the only Inspiron laptops to have this feature available are the Inspiron 15z Ultrabook and the 15R/17R Special Editions. You should check out the XPS, Latitude or Alienware lines of laptops, for this feature to be available on more systems.
The XPS 12 Ultrabook, that has a convertible screen and backlit keys as a standard feature, was recently released. It is worth checking out!
Hope this helps!