If you can see a faint image of the desktop than your LVDS cable is probably good. Since you replaced the inverter cable and the problem persists then you may need to replace the inverter board or the backlight lamp. In some cases the logic board can also be the culprit (when the unit was dropped causing an electrical short in the hinge and blowing the logic board inverter system or a damage caused by a liquid spill)
Habitually the first troubleshooting step is to connect the MacBook to an external monitor to check for a graphic card issue (when you don't have any video on the internal screen). In your case I don't think the graphic card is affected cause the problem seems to be a screen lightning power issue. Not easy to troubleshoot when you don't have known working parts to swap. A complete display swap would probably solve your problem but you may begin by buying an inverter board and check if you get a screen lightning. Not a bad idea to bring the MacBook to an Apple Store and ask the guys what they think the issue could be.