2008 Mac Pro powers off before loading

First thing I would suspect is a bad hard drive. See if you can run the Apple Hardware Test.

Use Apple Diagnostics to test your Mac - Apple Support

If you cannot boot the AHT from the hard drive, then you will need to use one of the original DVDs which shipped with the computer to run the AHT. Unfortunately the diagnostics don't detect all types of drive failures. I can provide instructions for creating and using a bootable Linux USB stick to check the health of the drive, just let me know if you are interested in this option. This option also will tell you if your Mac can otherwise boot and stay powered on.

Internet Recovery is NOT available in your model’s ROM, so you will need to explore this list of other possibilities.

The way you launched the required Utilities (including Disk Utility and Installer) when your computer was released was to use the ones on the Release software DVD. if you have a model-specific version for your model (unlikely) or a Full Retail 10.6 DVD, you use its Utilities, boot and install that version, then use Software update to get to 10.6.8 with all updates, which is the version that can reach out to the Mac App store and download and install a later version. 10.11 El Capitan is a recommended waypoint, even if you expect to install a later version, because it has an improved Mac App Store that makes getting later versions much easier.

The next source of Utilities is the Recovery Partition on the boot drive. If your drive spins up, even if not MacOS bootable, it may still have a usable recovery partition. To get there, try invoking recovery with Command-R or hold Alt/Option at startup and see if the recovery partition shows as a potentially bootable drive.

The next source of Utilities to consider is any MacOS 10.6 or later versions on any additional drives or clones you may (or may not) have lying about, even if they are from another Mac. You can use those Utilities to ERASE a new drive, and start the installer to place MacOS on the new drive.

The next source to consider is a Time Machine backup drive. Versions from 10.7.3 or later are said to contain a Recovery Partition that could be used to ERASE a new drive and run Installer to place MacOS on a new drive.

IF you have a different Mac, you can use it to download MacOS install image, then interrupt the process and create a BOOTABLE USB-stick Installer/Utilities stick. BOOTABLE is key, because the way you will install from this USB-Stick is to BOOT the USB-stick, and use its Utilities to ERASE your drive and start the Installer. here is the article on bootable USB-Stick Utilities/Installer:

What you need to create a bootable installer

• A USB flash drive or other secondary volume formatted as Mac OS Extended, with at least 14GB of available storage

• A downloaded installer for macOS Big Sur, Catalina, Mojave, High Sierra, or El Capitan.

from:

How to create a bootable installer for macOS - Apple Support

https://support.apple.com/en-us/HT201372

NB>> if you name your incoming USB stick exactly MyVolume, you can copy and paste the very long Terminal command from the article directly into the Terminal window, without having to change anything.

The solid Apple is not in the computer when it powers on. Seeing the solid Apple after a cold start says your Mac is working.

The solid Apple is loaded in the first "blob" of software from a known location on the drive. Next up requires lots of files by name, so the File System attempts to Mount the drive. If the drive has directory damage, a disk check is started. at the end of this disk check, it the drive has not been fixed up enough to Mount the file system, your Mac has nothing else it can do. So it powers off.

Your Mac is working. Your drive is functional. But its directory is not happy.

Try Command-R. It may get you to Recovery, from where you can attempt further repairs or a re-install of MacOS.