I have just read that the short beep on the dvm can be capacitors charging!
And the overall resistance should be 0,00 Ohm for a short.
I have changed the two biggest caps and the two big transistors on the psu. One of the caps had a bump on the top.
So it could have been a psu problem after all.
It is now fully rebuilt and calibrated. All the voltages are present.
Still I am afraid to connect my synth to it and test.
Is there a way to test the psu itself under load without a specialist equipment?
Please advice.