Guess what? Yep, it’s more bad capacitors.
See the BadCaps forum thread for more details. The problem is on the power supply board. Replace all the 220uF and 470uF capacitors, and don’t forget the single tiny 47uF next to the transformer. Don’t forget to screw the ground strap back in before plugging the power supply board back in.
Also, if you get the backlight connections backwards, the backlight will power on for 1 second and then shut down. The correct wire colors from top to bottom are white, pink, black, gray, in both sets. Note that the top set of black and gray wires connect to a white and pink harness, this is unexpected but is normal.