It's not a bulb, it's an EL panel. They don't really ever burn out, but can grow dim over time. The problem is possibly with your Light button; a small arm that pushes a microswitch on the circuit board sometimes breaks off. If it no longer seems to "click" nicely that's likely it.

If it still seems to press normally, then it's possible (but unlikely) that there's some grungle inside that could be preventing the EL panel from making proper contact with the circuit board (it's just a press fit). However something else could be burned out or broken.

If you really want to, instructions on how to open the remote (or the MX-500) have been posted several times before (look in the Universal Remote Control Inc. forum). However if you aren't technically or electrically inclined I would strongly suggest sending it into URC... the case can be easily damaged when prying open.