I am afraid that there isn't any shortcuts into finding where the problem is, because as well as it appearing as though there is a bad joint somewhere there is also a possibility that its a component that has partially fractured.
The best way to carry out a test is to with the aid of a PLASTIC OR NON CONDUCTING ROD carefully prod (slightly push on) each of the higher standing components and this will give an idea of the fault location when (hopefully) the set suddenly comes on.
It should be mentioned that the chassis you refer to is notorious for faults in the frame timebase circuitry, and especially around the chip (I/C) mounted on a vertical heatsink which can suffer from bad joints at its base, that is as well as it blowing altogether due to the notorious C926 fault, another place to check as it sits near to the I/C.
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