start off by doing what Apple suggest:"Power, but No Video (Computer begins to power up, the fans and hard drive spin, the Caps Lock key lights up when pressed, but there is no startup chime or video.)
Note: Examine the display carefully. An image may be barely present on the screen, but with no backlight clearly illuminating the image. In this case, the system is working properly except for the backlight. Use the Display: Dim Video troubleshooting section to resolve this issue.
1. Reset the power manager (SMC).
2. Try connecting an external display to check for intact video signal. If external video appears, check the system for any pending software or firmware updates and update accordingly.
3. Verify that the LVDS cable connection is properly seated to its connector on the logic board and that the cables are not damaged.
4. Remove the display housing and check that the flex connection is properly inserted, aligned and seated in its connector on the panel. Misalignment can cause multiple video issues. During insertion, the connector should be perfectly straight, not at an angle, and the connector should slide into its mate in a flat position, parallel to the LCD panel, not obliquely.
5. Replace the display assembly.
6. Check all cable and flex connections to the logic board. Try restarting.
7. Replace the logic board.
Step 7. is the one I would wait with. Now here comes the important part. Are you capable of measuring the backlight fuse as well as the WLED driver to see if those function. Those are the parts that are responsible in part for the backlight. Hope this helps, good luck.