I had this EXACT problem. replaced digitizer, screen worked fine, and then backlight went out. I had disconected the logic board while power was on, I had no choice because I had powered up without the digitizer connected to test it and as I found out, there is no way to turn power off without the digitizer connected. Above peopel suggested they created a short with the screwdriver, but I was meticulous, only using plastic.
Its a software issue, the logic board does indeed get "confused", and think the backlight is on when its not. Soft/hard resets didn't work, UPDATE THE FIRMWARE. for me it was rfom 3.2 to 5.01, as soon as I updated it the backlight came back on. If you dont need an update, try a factery restore and then an update.