The first step to finding the cause of a backlight issue is figuring out what type of failure is causing there to be no backlight, a short to ground or no boosting. In this case, we have no short to ground on backlight output. This means that backlight output is either not boosting, or not getting any power at all. Measuring both sides of the coil, we see that we have 8V on one side and 0.2V on the other side. This tells us that we have a bad backlight coil, as the output on the coil should be much higher than 0.2V.
How do we fix the issue?
We first replace the coil with one from a donor board. After doing this, we see that we are now getting 8V on both sides of the coil. This is still not good enough to produce a backlight. After conducting another visual inspection, we determine that the jumper that we had run to repair a bad feedback trace was not properly soldered. After correctly soldering this jumper, we see that we have backlight again.