OS X Snow Leopard won't boot into Recovery mode, need to reset admin password

It is possible to download a Mac OS X Snow Leopard Install DVD ISO file from the internet. After downloading, you should run the following command to verify the SHA256 checksum.

shasum -a 256 snow\ leopard\ install.iso

The output should be as shown below.

cbeeb2378c40b20a9b06236f567de593e9030a0a865515b50cf6d35833e25cd5  snow leopard install.iso

I used my actually Snow Leopard DVD to verify the checksum. See this answer for an explanation.

You can either burn the ISO to a DVD DL (DL=Double layer) or create a USB flash drive installer. Instructions for creating a flash drive installer are given in this answer.

Mac OS X Lion, 10.7 was the first OS to introduce the Recovery Partition.
Internet Recovery came later still, in Macs introduced in 2011 [iirc].

That means your only way to boot from other than the regular boot drive is to either use the original Snow Leopard disk, or attempt to boot it from a USB key.
That in itself may depend on precisely which Mac Pro it is. Personally, I have never managed to boot a 2008 3,1 from USB, though others say they have succeeded. I've successfully booted 4,1 & 5,1 Macs from USB. I've never owned a 1,1 or 2,1 to test.

As it is a Mac Pro, you have the potential of a third option - you can drop in a new drive with either a full system on it, or a bootable installer.

If all you need to do is reset the password, then that can be done on older OSes from Single User Mode...

From MacYourself - How to reset your Mac OS X password without an installer disc

1. Power on or restart your Mac.
2. At the chime (or grey screen if your chime is turned off), hold down Command+S on your keyboard to enter single-user mode.
3. This step is optional, but it’s a good idea because it checks the consistency of the hard disk before moving on. At the prompt, type fsck -fy and press Enter/Return. Wait for the checks to complete before going to the next step.
4. Type mount -uw / and press Enter.
5. Type launchctl load /System/Library/LaunchDaemons/com.apple.DirectoryServices.plist and press Enter.
6. Type ls /Users and press Enter. This lists all of the usernames on the computer – helpful if you don’t know or remember what these are.
7. Type dscl . -passwd /Users/username password and replace “username” with one of the users displayed in the previous step. Replace “password” with a new password of your choice. Press Enter.
8. Type reboot and press Enter.

If you cannot boot into recovery mode or internet mode, this issue may be hard to tackle.

Before we start, please be sure to back up any files on your Mac.

Back up your Mac with Time Machine - https://support.apple.com/en-us/HT201250

Please also note that this method is not encouraged by Apple, but usually works. You may also see some effects such as loss of data or damaged OS. However, these issues do not occur often.

To begin, restart your Mac. When the start-up chime rings and the white screen appears, hold the Command ⌘ + S keys. This will take you to Single User Mode. Be sure to do this before the Apple Logo appears. Hold the two keys down together until a black screen appears. You may then let go of the keys. A large number of lines of code will automatically appear on your slowly, do not do anything while this happens.

Wait until you think the commands are fully done appearing. After that, enter the commands listed below one by one. Be sure to click the Enter or Return key after each command.

mount -uw/
rm /var/db/.AppleSetupDone
shutdown -h

That last command should automatically shutdown your Mac. If not, proceed to shut it down manually. After your Mac shuts down, power on your Mac. Once the boot has finished loading, you should be greeted with a screen to either to choose your language of preference and continue with Mac setup or if on a macOS X Server (10.6.8), the ability to create and register a new server. (Please Note: Creating a new server will not result in a fee.)

Try to use the link below for any extra information:

https://www.iseepassword.com/reset-mac-login-password.html

If this doesn't resolve your issue, please look at the other answers to your question.

I hope I helped

Cheers, John Williams