New development --
After a careful close examination and some fiddle-around measuring the connectivities and voltages, it cameto be that a fine trace under the belly of a transistor seemed broken - measuring different voltages at its two sides. After connecting it with a jump wire, as shown, now the low battery sign is gone, and when pressing the power on button, the LCD backlight lit up!
Also, the +ve rails of the two op-amp chips all give 5V (presumably this is a good one?), #7 pin of the audio amp chip gives 14V (correct), the Vdis/Vadj pin of the voltage regulator give 2V (enable) and in turn, its Vout gives 5V (also correct)!
All good. However, the front panel does not respond further and there is no radio or noise coming out of the speakers. And it can not even be turned off by pressing the power button.
Also, the voltage regulator chip is very hot (it does not have a heatsink with it).
Is this closer?

