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if i understand correctly, in the case of c7771 the issue is that the capacitor lost some of its original capacity, that cap is for stabilizing the operating voltage 1.05V for the CPU, so when the controller for that 1.05V is trying to set it to the exact value, it has some time limit , and also is looking for for voltage stability, and if the output buffer cap doesnt have the designed capacity the voltage could drop lower when the cpu starts to load the circuit.
Also im not too sure about this, but once i measured the removed bad cap, after replacing that the board was working fine, and outside the circuit i measured higher capacity than should be for the bad cap, i measured it with a Fluke 116C, that is a like a 250eur multimeter, i think it is pretty accurate, so im not sure that is possible for a cap to have more capacity over time, typically caps are loosing capacity, but if that is possible than the controlling circuit might think there is short on the circuit. also it could cause voltage rippling.
The c7771 is a tantalum capacitor is electrolytic capacitor, which i think is has some non-solid material inside, which can dry up, that is causing the change in capicity.
if im wrong in any of the above correct me.
So i guess someone working on the board trying to find the cause had a general knowledge and experience in electronics, and that u should suspect capacitors to be blown, dried out, shorted in general, and maybe a thought that a 1.05V is a very low voltage even in micro electronics, but at the same time it is supporting i think abuot 20A for the CPU, so that line probably more sensitive.... i guess this kinda thinking was behind finding the issue.