How to add songs into iPhone from a new computer?

How to add songs into iPhone from a new computer?
Normally I use my laptop to add songs to my phone, but my laptop is dead.
So I download itunes to my desktop, but I'm unable to add any songs.
What should I do?

-I have backup and transfer purchase to this desktop.

Why not use iPhone/iPad/iPod transfer which can transfer files from PC to iPhone/iPod/iPad? It supports all iPad/iPhone/iPod verions.
Here is an example about to how to transfer music from PC to iPad, I think it will be helpful to you.
http://www.ipadmanager.net/guide/transfer-music-from-pc-to-ipad.html

As far as i know or remember, it's just not possible right now.
simply cos the iPhone (or iPod) could have music that was bought off iTunes with DRM protection…
the only suggestion i could give is to just put all the songs from the other computer onto a usb stick or cd, and transfer them over to the new computer.otherwise i'm afraid, apple just don't allow it.

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