I've replaced several LCD backlights, it's not an easy job to do. On some LCDs it is very easy to damage something and getting the diffuser sheets lined up properly can be a chore. If you're handy with small stuff give it a shot. With a laptop that age you should be able to source an LCD for not much more than the cost of the CCFL.
One question, have you ruled out a bad inverter?
One question, have you ruled out a bad inverter?