My problem was similar. The backlight would remain lit when the screen was opened less than about 45 deg. - any more than that would be hit-or-miss. For the last couple of weeks I've had to repeatedly open and close the screen and carefully finesse the last 50 deg. of arc to sometimes have use of the screen. A few days ago I attempted to troubleshoot the problem using the excellent step-by-step guidance found on this site: [guide|1495].
Completing steps 1 to 12 permits removal of the track pad and keyboard, exposing the internal circuit boards and wiring. A careful inspection of the wiring to the screen (after vacuuming an accumulation of dust debris from the circuit boards) revealed no obvious defects. Skipping to steps 36 and beyond exposed the wiring within the screen (display). Again, no obvious faults. Reinstalling the battery and connecting the keyboard wiring allowed for further troubleshooting by carefully prodding screen wiring. Again, no success in uncovering the screen problem. Finally, with the battery again removed and the keyboard disconnected, the screen hinge mounts were removed (steps 33 and 34). Under the left hinge (step 34), a piece of foam rubber banded in fine metal mesh was discovered compressed between the hinge mount and insulated wiring to the screen. A nearby crack in the insulation of one of the wires was noted. The small piece of mesh-clad foam rubber was removed, the hinge mounts reinstalled, and the battery and keyboard reconnected. The screen backlight remained lit throughout the full range of motion. It's been two days since this "repair" was completed and all remains well.
In summary, the screen backlight problem was probably the result of electrical shorting due to the metal mesh contacting the wire through damaged insulation. Removing the left hinge mount (step 34) allows for removal of the mesh covered foam rubber hold-down. In my case no repair of the damaged wire insulation was required.