Assuming that you are confident that the backlight is 3.3V....Before going too much further effort-wise, I would test the backlight. I can't tell from your picture if the two backlight leads are now isolated, but if they are (or you make them isolated), what happens if you connect 3.3v through a current limiting resistor, and to gnd. The backlight LED should light up. (assuming you have +/- correct - and you can test reversing them without damage because it is a diode and you are limiting the current), if it doesn't, the backlight led is fried and I don't know what you can do other then replace the display.
That's what I would do anyways.