Just fixed a Compaq CQ61 with a problem where Backlight came on, usually, at boot up but then flickered and went out.
Found issue was the magnet that switches backlight inverter on/off when lid is closed. It had fallen out of its slot on bottom frame of LCD panel and was magneticaly held in place over Inverter coil. Rather than put it back in slot, I just removed it permenantly. Backlight now fine.
How to get at it . I guess my laptop had been taken apart befor I got it as the 2 screws at either bottom front edge of LCD frame were missing. So I just levered off the LCD surrond, pulled it away and the bottom fron LCD cover comes away with the frame. Behind this cover is the LCD inverter, a sliver magnet was just lying on top of the inverter coil. I just removed it. If you find same and want to replace it there is a small slot in the bottom of the LCD front frame. Suggest you glue it in to prevent it coming out again, but remember it is NOT needed if you do not care if backlight stays on when closing laptop lid.
If the 2 screws are in place, possibly behind small rubber plugs you may still be able to get at them at an angle. Else searching the net there are instructions on stripping down a CQ61 laptop.