Hardware test program for Mac Pro 2009 ?

It may be difficult to obtain a model-specific Apple Installation DVD that includes the AHT for your 2009 Mac Pro.

I am assuming that you have already tried the following:

1. Held down the <d> key while rebooting your Mac Pro.
2. Held down the <option><d> keys while rebooting to access the AHT from Internet.

If that is the case, see if any of the following articles can help:

• Use Apple Diagnostics or Apple Hardware Test - Apple Support
• How to Use Apple Hardware Test to Diagnose Mac Problems - OSXDaily
• Apple Hardware Test (AHT) - GitHub

The Apple Hardware Test D-for-diagnostics feature from your Boot drive was supported by the .diagnostics folder (about 8.8MB and invisible) installed at:

/System/Library/CoreServices

... on your original boot drive. But any drive replacement or ERASE over the years would have removed it, and there is no software responsible for putting it back.

It is in a similar location in the minimal System on the original Installer DVD, if you still have that.

If you extract the correct version from the DVD or from GitHib, you can also choose to place the .diagnostics folder back where it is "supposed to be" on your boot drive, and the D-for-diagnostics key will work again from the Boot drive.

This must be done while booted from some other copy of MacOS, because CoreServices in the running system is locked up tight. To make it even more difficult, invisible files and folders are difficult (but not impossible) to manipulate with Finder.