Thanks for the suggestions. Made a little progress. Also have some additional questions.
Firstly I have to say that I found handeling the PSU board in general very difficult. It is very crowded and not possible to completely turn it over. The reason is that the main input is soldered to the power plug connector and cant be removed easily. So my first question is - if you fix PSU units - do you desolder the main power wires to get the board out of the housing completely simply for better handling ?
Anyway I checked as many components as possible and indeed found one larger capacitor on the secondary side that is definitively shorted. So far I have never recaped anything but I want to do so in the future. I have a mainboard which needs new capacitors so I want to learn to do this in the future but I will need sufficient time. So a second question is then - would I replace only this faulty capacitor or would you suggest recapping all electrolytic capacitors or even ALL capacitors incuding metal oxide ones (seems a bit of a dounting first recap job) ?
For the meantime, I came up with a solution. I have a working (also quite old) ATX PSU as well as an ATX to AT mainboard adapter. This adapter cable also has two additional wires that can be used for a power switch. Tried that and indeed the PC is booting! So now I know at least that the PC is not dead - nice!
Thanks again for the support