So, I bit the bullet and did what I have been considering for a while (but wanted to exhaust all other options before that): I've reflowed the NXP chip (i.e. U26).
This is because the seller of this meter mentioned they had dropped it, thus ending up with a broken screen.
So, I thought the impact may also have affected the connection between U26 and the board.
I am happy to report that, following the reflow, I am seeing a positive evolution: the 5V rail is now coming up and, consequently, the 2.5 reference voltage is present too.
Moreover, on pressing the power button, the LED beneath it turns on for a while, then turns back off, with the meter still drawing some current - from the videos I watched on Youtube, this is the expected behaviour.
Also, if I press the power button once more, the meter turns off (very little current draw from the power supply it is connected to).
The other good news is that, with the rotary switch set to Resistance, if I measure the current between COM and V terminals, I see very exact current being generated.
Moreover, if I press the Range button repeatedly, the current changes to very specific values (e.g. 100uA, 1mA, etc.).
So, at least some part of the meter is alive now.
Now, the not-so-promising observations (all this is done on the blind, as I have no working LCD):
- if I switch to Continuity test mode and short COM and V terminals, there is no sound generated (and I checked outside of circuit that the buzzer is working).
- if I set the rotary switch to DCV, for instance, and insert a lead into the u/mA or A jacks, the meter should beep to warn me I got the lead in the wrong place - however, I'm not hearing any sound.
- (still not sure if this is really an issue or maybe a red herring) the shorts on caps C46, C55 and C92 are still present.