Probably unlikely that a capacitor would have any bearing on this.
If you are going to order new parts, go ahead and cut the leads on Q2 the presumed NPN transistor so that you can better read it's markings. This also has merit, in that doing so eliminates what I will call the pre-switch for Q1. So after cutting it out, apply power once again with the 555 timer removed and see if the system stays OFF. If it does, there is a good chance that Q2 was either bad or the wrong part. If the system still comes on without the 555, then remove Q1 and see what happens. If it still comes on without Q1, then there is a serious bridge somewhere (hopefully not in one of the inner layers of the PCB).
Sorry for this long delay but I had no time to do Atari related things last week.
I did what you suggested and here are the results :
1) I cut Q2. It was a 2222. Then I removed the 555. The system still goes ON.
2) then I cut Q1. 555 still removed. The system stays OFF.
Does it mean that Q1 was damaged (maybe when I soldered it on the board) ?
Do you think replacing these 2 components will cure the issue or do you want me to do other tests before replacing them ?
I am still waiting for both components to arrive but when I have them, I replace them and tell you if the issue is still there.
Thank you for your help !