Old Mac OS X, cannot get admin access, boot safe or single-user mode, nor reinstall
Give this a try.  If you can get to single user mode you can remove the file that OS X checks for during boot to determine if the Mac has already been setup.  If it doesn't find the file then it boots to the setup assistant, which allows you to create a new admin user.

Try resetting PRAM:


Shutdown the Mac
While holding ⌘+option+P+R, power on the Mac
Continue holding all four keys until the Mac has chimed (restarted) twice, then release the keys and allow it to boot normally


If that fails, or you still can't boot to single user mode, give this a try.  Resetting NVRAM:


While holding ⌘+option+O+F, power on your Mac, after a few seconds you should be greeted with the Open Firmware screen.
Type and click return: reset-nvram
Type and click return: `reset-all'


Hopefully by now you can boot to single user mode.


Boot to single user mode (⌘+S while powering on)
Type and hit return: /sbin/fsck -fy
Type and hit return: /sbin/mount -uw /
Type and hit return: rm /var/db/.AppleSetupDone
Type and hit return: reboot


This should boot your Mac to the setup assistant.  From here you can create a new user account, which will automatically be designated as an administrator account.

Hope that helps.