That connector. P201 (on the power supply) that feeds the main board has 2 rows of pins, the ones you can see at the top of the socket, and a row below that you have to access from the back holes in the plug. So you're reading PWR-ON correctly, but 24V is the pin below.
Of most interest is the pin designated DRV-ON, which is the backlight-on signal, again 3.4V approx., which I suspect you'll find missing. The LW series all seem to fall down in this respect. A cook-up in the oven will likely sort it (bad ball joints under the micro) and on your model the heat-sink on the micro is just held on but a bit of silastic at the sides. One I cooked didn't respond, so I put a weight on the heat-sink and tried again, but still no luck.
Those that do recover only last about 5 months, and the customer goes head-hunting for guess who. Bruce