iTunes accidentally deleted on iMac G5 with OS X 10.4.11 - how to install iTunes?
Your downloaded DMG should work, but assuming you still have the Mac OS X Tiger install DVD you could try the following instead:


Insert the Mac OS X Tiger install DVD
When Finder opens the Mac OS X Install DVD window, scroll down till you see the System folder
Navigate to System > Installation > Packages
Locate the iTunes.pkg and double-click on it
This should launch the iTunes installer
Follow the steps to see if you can install iTunes. 


Assuming you can, after doing so use the Apple > Software Update option to update it or launch iTunes and go to iTunes > Check for Updates option instead.