The damaged disk is and has been removed, it is out of the picture.
I replaced it with a new and undamaged hard drive.
On that new and undamaged hard drive, I installed El Capitan from the Installer on a USB Stick.
Then I erased the USB Stick and created a bootable installer on it once again*.
Then I tried to boot the mac from that newly set up USB stick. But the system won't boot from that. I can only boot the new internal system. (In that new internal system's preferences, the USB stick isn't even recognised as bootable.)
Now if I take the new hard drive with the new system on it out of the mac (physically), so that no system remains in the mac, I can once again boot from the USB stick. But only then. (And to no avail of course, as without the new system present, I can't restore the previous system on it from Time Machine).
Briefly put:
— MacOS present on (undamaged) internal drive —> no booting from USB Stick.
— NO MacOS present on any drive —> booting from USB Stick works fine.
*(because just as you had told me: If you install on the internal disk, the Installer will be erased at the end of the process. Since I need an external drive to boot the Mac in order to be able to restore the previous system from Time Machine to the new system on the new hard drive, and since I have no other means to create a bootable second system internal or external, I created a bootable installer on that same USB stick)