that this isn't a DIY job, but provided you are reasonably competent with a small set of screwdrivers and a soldering iron you can do it.
That bit about the soldering iron usually scares people off, and I definitely don't recommend that you try this repair unless you feel pretty confident using such a tool. The problem may not be the backlight by the way, it might be the inverter, but either way you can do it, and as your machine is probably fairly well-used you may consider it worth a try.
You'll need to identify the exact type of cold-cathode tube for your machine, and the best way to do this is by exposing the existing one. Then contact a backlight supplier - there are lots, but
click here is a very good one, and take it from there. The keyword involved in carrying out this repair is CARE - one false move with the screwdriver or soldering iron and you could be looking at a new screen instead of just a backlight/inverter.