Screen goes black, but computer is still running---

Sounds like you did right by replacing the inverter and cable. I would question the source of the parts. Also, hook it up to an external monitor to eliminate the possibility of any logic board or GPU issues.

"This is definitely the WXGA lamp, the light source for the LCD panel. I just changed mine and all works fine now.

The short and more expensive way to fix this is simply replacing the entire LCD panel - which I would not recommend.

The long and much cheaper way is to replace the actual 13.3 inch WXGA lamp located at the bottom of the panel. I must warn you that it is an absolutely daunting task because not only do you need to remove almost 30 screws to get to the LCD panel, but you have to carefully remove the tape at the bottom of the panel and carefully extract the lamp from its housing.

Re-assembly is also tricky because you need to use high temperature tape after you install the new lamp on the LCD panel, and then re-assemble everything back correctly (especially the wires).

I would recommend using one of the step by step guides for the LCD panel brackets, and once you free the LCD panel, just remove the 2 bottom screws (one on each side) for the housing cover, and then you have access to the actual housing. One other note is to make sure that your new lamp's cords are long enough in order to reach the inverter once re-assembled.

Good luck with the DIY, definitely among the most challenging (but most rewarding) that I have attempted doing!"

"Does the screen look dim when it is working (at full brightness)?

Does the light source appear to flicker a bit and flicker just before going out?

I assume you checked your energy settings and reset the PRAM/NVRAM or SMC as needed depending on your model. Here's links to Apples TN's Resetting PRAM & NVRAM & Resetting the SMC.

Also, does your clock setting appear to get lost? when your NOT connected to either a wired or WiFi network when you first start up your system. If so, your PRAM battery needs replacement."

"Plug it into an external monitor and tell us what it does, so we know if there is an issue with the board. This lacks a GPU, so it’s typically going to be the screen but in some cases, it can be due to a bad motherboard.

The next thing you want to try is resetting the SMC and PRAM and see if it helps.

If it turns out to be the internal only, it’s either due to a bad cable, screen or motherboard. The cheapest fix is to try and reconnect the LVDS cable and work your way up to the screen. If neither the screen nor a LVDS cable help, your board needs repair.

The LVDS guide can be found here and the screen guide can be found here."