Why? Because if you install iTunes and plug in the iPad the sync will sync what's on that PC to the iPad and not from the iPad to the PC.
This area is well discussed, Apple has web pages about how to backup and restore your iTunes library to another PC and I'll not duplicate that here but I will make a suggestion.
Install iTunes on the new PC and then research how to use iRip if you are not able to backup and restore your current iTunes library.
The Hard drive on my Laptop Windows Vista Home Premium is failing. This is the Laptop that I was using to Synch all my iTunes songs with my iPad, 3rd Generation, Wireless. Can this iPad be setup with another Laptop with Windows XP Pro for the Synch of my iTunes songs? If so, can someone please provide the procedures to do so.