Update: I got the new LED screen but they actually had a different inverter attached to it. So I removed the old one and the new one doesn't really fit, but the screen works.
One weird thing though, whenever I press the brightness button there is a pretty big change in brightness from the highest setting to the second highest setting.
For example, the overlay that pops up:

When the brightness is at its highest setting, it looks fine. But when I press the button once to decrease the brightness, it is a lot darker than before. If I keep decreasing the brightness, when it reaches the halfway point the screen is just barely visible, and does not change when I go all the way down to 0. I'm guessing this is not normal, any ideas?
In any case, I am going to buy the R267J cable mentioned in this thread because of this problem and because the inverter barely fits. Does anyone know if it is compatible with the B156XW02 v.6 screen?
Thanks.