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0.58 would indicate an issue near the LED driver for the switch trace. Inspect the LED driver for corrosion and make sure the A5 ball and the pads for balls 6 and 7 have continuity for feedback and switching.
::18 has 3.3v and ::14 sits at 2.6V (This is with a screen)
What should BKL_EN @ R7731 be?
I'm getting 4mV and at C7712 I get 8.59. (which becomes BKL_EN via R7731 right?)
I'll remove the LED driver and check all the traces if needed, but would prefer not to waste the chip if possible.
Serves me right for not measuring when it was off though, but the chip looked toast.
BKL_EN should be around 2.7v . You had 3.3v then 0.04v, that is confusing. There is something simple missing here, bad feedback or switch, I imagine it is the switch trace that is missing due to 0.580.
0.511-0.546 is normal, 0.450-0.511 is bad feedback, over 0.556 is usually switch trace not making contact.
Start from zero...
If U7701 already ripped, check continuity from all its pads to other components.
Next, aolder new chip and post voltages at Q7706/07 and U7701, power and controls.
Change/resolder U7701.
Cjeck again EN and PWM, as its power too.
Check every resistor from return lines.
Measure on diode mode all 6 lines; you must get almost same value, no open line permited.
Don't forget XW7720.
And test known good assembly screen+video cable...