Have you tried using a PRAM reset? This can often resolve issues similar to the one you are describing.
To reset the PRAM:
- Shut down the computer.
- Locate the following keys on the keyboard: Command, Option, P, and R. You will need to hold these keys down simultaneously in step 4.
- Turn on the computer.
- Press and hold the Command-Option-P-R keys. You must press this key combination before the gray screen appears.
- Hold the keys down until the computer restarts and you hear the startup sound for the second time.
- Release the keys.
You will know the PRAM has been reset when the Macbook restarts and you hear the startup chime.
If this does not work, it could also possibly be an issue with the Inverter cable, LCD panel, or the main logic board. Since both of these parts also play a role in the backlight functions of the Macbook.
I would suggest swapping out the inverter cable first, to verify that it is not related. If that does not work, then it also could possibly be the LCD. I would suggest contacting iFixit to see if they can send you another inverter, as it is possible that it could be defective. But I would have my doubts about the inverter malfunction since the new one did allow the backlight to return. I would only use this as a last route of diagnostic legworks before coming to the conclusion that it would be logic board or LCD panel related.
If it gets to the point where you are faced with swapping an LCD, I would suggest taking it to a local AASP (Apple Authorized Service Provider). Even if it just for a diagnostic, it can save you time and money. If swapping the inverter / inverter cable does not fix the issue, then the issue is more than likely logic board or LCD panel. As both of these parts are fairly expensive, and you would need one or the other to use component isolation to figure out exactly which one. You wouldn't want to buy an LCD just to test, then realize that it didn't work. At a service provider, they would have access to these parts and would be able to tell you exactly what it was, they would more than likely charge you a minimal diagnostic fee, but you wouldn't have to buy an LCD or a Logic Board to test your Macbook. Once you have a diagnosis, neither of those parts are extremely complicated to replace, and you could more than likely perform the repair with minimal difficulties, since you already have experience replacing the inverter.