James Sweet sez:

Most of them use CCFL tubes. If you open it up and look at it, it should
be obvious. Inverter failure is common but the tubes can wear out too.

To add a little detail...

The CCFL is a thin (some as small as 1/4 inch diameter) fluorescent lamp that
runs the entire width (usually) of the bottom of the screen. It's usually
taped tightly to the screen with copper tape and not always easily
accessible. I'd bet it's the driver board (inverter) that has failed. This is
much more accessible and I'd test the output of this before tearing apart the
display to get at the bulb.

Good luck,
--
Al, the usual