Now, I don't even hear a clicking sound at start. I removed all the blades, still no click. I see only 1 yellow light (next to the PCI connection), but no red light (next to Ethernet).
Will it help if I replace the PSU, or is this cube dead forever ?
you probably shorted the cube when you opened it up

Is there a way to know exactly what's wrong ? Is it usually only 1 light on when you plug the PSU. I don't have another PSU handy to check right away. Will have to get another one from the store if you think that can help.