MacPro 4,1 starting with grey screen after SMC and PRAM resets

Thanks once more Grant. I'm trying to do that, but Create a bootable installer for macOS - Apple Support instructs me to make sure it is an installer app, not a .dmg or pkg. The only indication on how to get that app that I find is https://apple.stackexchange.com/questions/254223/how-to-convert-a-macos-installer-pkg-into-an-app-to-run-it, but that didn't work on any Mac I could get my hand on: pkgutil --expand InstallMacOSX.pkg installmacosxpkg returns Could not open package for expansion: InstallMacOSX.pkg. I know this isn't really the topic here and I'm happy to start another thread, but maybe there's an obvious answer to this?

Great, that worked! Thanks so much. Now I have the installer open, and would try and install the system on an empty internal disk, intending to then migrate from the previous system disk, then clean install on that previous disk, and finally migrate back to that one (since it is the only ssd I have for that 15 years old machine). Or is there a smarter way to repair the system without losing settings, apps etc.?

Sounds good. Now, a new problem (one at each step … ) — I created another bootable installer (on the very same USB stick), and it boots fine on another mac but not on the one in question (the MacPro). However when I take out the system drive from that MacPro so that no bootable system remains in the computer, it does once again boot from the USB stick. A riddle to me in itself, it makes it impossible to boot from it in order to restore the previous system from the Time Machine backup to the new system. Any idea why? Thanks, once more. 

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)

Hello Grant,

thanks. I'll attach it.

Sorry, I wasn't very precise: I do get a grey screen but nothing beyond that. It remains grey, no options, nothing at all on it.

There is neither a wait cursor nor anything else, just plain grey.

Yes. How do you suggest I access the system preferences without booting the system? Perhaps in target mode, changing them manually?

That would have been smart. I was too confident, and now even the hardware reset doesn't allow for another boot, so unless there is yet another trick, I can't.

I do have another Mac, yes. A MacBook Pro 2018 (Intel), running Sonoma 14.5. No Windows, and I wouldn't know what a developer thinks like. (I'm happy to learn though.)

So I reckon. It would still be excellent to be able to use the Time Machine backup in some way. Ideally to restore the startup volume (on a new drive of course). Would that be possible somehow?