Excuse me for being sarcastic, but very often almost all problems which can occur are reduced to "capacitor" problems only.
Many (almost all?) forgot, that there are also semiconductor stuff in it, and that thermal load will shorten lifetime of these components, too.
Also, I suspected also the dead battery, because someone here already asked what dependancy are related to the batterty / what function is covered by the battery also.
And finally, it is not necessary to be the upholder of moral standards, I agree that this board should be used for exchanging information and (sometimes) fun only, yes.
I wrote already that I replaced for test purposes the power supply and the bad "start" behaviour did not changed, so I can exclude the power supply itself as a reason.
Last but not least for further examination, I need a schematic diagram, or even better, test points with voltage values or oscilloscope screen images (can be often found for monitors also).
I fear test points with voltage values and/or oscilloscope screen images (for comparison purposes) will not exist, and I'm unsure if I am able to use a schematic diagram for diagnostic purposes (I studied computer science, not electrical engineering). Finding a contamination with weak acids from a bad capacitor should be easy if the circuit traces are (visually) affected, but I am not an expert in circuit traces.
May be the hint about the diodes (the ones in row) is important too, will look for these also.