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If 12.96 on just the charger, that is a little high. Might be worth replacing Q7130 and Q7155 with the ISL6259 at the same time to see if any change. Also check resistance between pins 17/18 and 27/28 of the ISL6259 first.
Don't have one. If you're talking about the intermittent backlight fault, it appears to be an issue when the CPU gets too hot it shuts off backlight. We saw about 30+ at once for the same issue tried multiple different things (coils, diodes, filters, etc.) and nothing seemed to fix the issue.
Very likely the CPU is dead. When those fets short, they send 12 volts to the CPU. The dropout issue is only if the board is randomly shutting down not if PPBUS is directly shorted to ground. This sounds like an RIP.