This could be the inverter, or the CCFL it supports. I would replace both at the same time or you may be tearing the notebook apart again soon.
Note that inverter and CCFL replacement is a common repair task and many repair shops will do this for a flat rate, plus parts. And because these shops do this almost every day (or perhaps several times a day) they have the tools, know-how, and experience. Plus - they are then responsible for any collateral damage - and that is often the key. I know how to fix the brakes on my truck, but I would rather have someone I can sue do them, should something go wrong.
As far as the manual, it will certainly show you specifics if you choose to attempt this yourself. But a quick Bing Google search will show you many tutorials. Replacing the parts is not hard, getting access to them can be tricky.