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

if you have another Mac, you can get access to some downloads, such as MacOS 10.11 El Capitan, or 10.13 High Sierra. You may be able to unpack it and make yourself a bootable MacOS installer on a USB-Stick.

The earliest MacBook Pro 2018 shipped with MacOS 10.13, so it might actually be able to boot from a hand-made 10.13 USB-stick installer, PROVIDED you had a chat with Recovery Security Utility to allow booting from external drives.

this can, in theory be done on a Windows machine, but requires some developer-caliber software, and results are not guaranteed.

You need a USB-stick of size at least 8 GB for this exercise, that is completely erase-able. later versions required a larger, at least 16 GB, USB-stick.

oh put that way too complicated stack exchange procedure away.

download the .dmg.

double-click to open it. the disk image mounts. it contains a .pkg.

double-click the .pkg to open it. It runs and PLACES the Installer App in the /Applications folder. (it DOES NOT INSTALL)

The 'make a bootable installer USB-stick' scripts REQUIRE that the Installer Application be present and located in the /Applications folder. The tools you invoke with those complex terminal commands are INSIDE the Installer image.

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Make sure you have named your USB stick exactly MyVolume.

Open the article with the 'make a USB stick commands'. Open a Terminal window. Select the entire Terminal command from the article and Copy to the clipboard. Click in the terminal window and PASTE the entire command in the terminal window. Press return, and you are going.

if you install on the internal disk, the Installer will be erased at the end of the process. if you install anywhere else, the Installer will be retained, and you can create a USB-stick installer later, and just set it aside for emergencies. Because your Mac Pro 4,1 does not have built-in recovery, making the bootable installer of El Capitan or later would be a good thing to do.

Booting from an external drive us a great way to attempt to rescue a failing drive, because the criteria for Mounting a drive are far lower than for Booting from the same drive.

The long term solution to retaining your files is to make Time Machine backups. After the initial backup, they just happen at low priority in the background, and the Time Machine backup is MUCH more likely to be there when you need it.

A drive that will not tell Disk Utility it make&Model, and a reasonable non-zero size/capacity, is the definition of dead.

It can not even be erased, so it is a door-stop.

as it was dying, it was teasing you by occasionally working for a while before it quit again.

did you get a chance to enable TRIM?

are you booting from an alternate drive?

The code supporting option key boot is all in ROM.

if you can't get a gray screen, your Mac has hardware problems.

The code that runs Recovery on that Mac is on a drive -- it does not have a ROM version of Recovery.

You should also get a 'wait' cursor, but that does not always happen. Then it discovers possible bootable drives over the next several minutes and adds an icon for each potentially bootable drive it finds. When it has scanned through everything once, you usually get an Ordinary pointer cursor.