My old computer is broken... is ther a way to sync my phone to my new one without loosing all my music?

Hey Brooke082688,

There's an answer to your question in the following document:

Using iPhone, iPad, or iPod with multiple computers

http://support.apple.com/kb/HT1202

You can either transfer the purchases to the new computer, or you can set the iPhone to manual mode and add the new songs while keeping the old. The article will go over how to do both options.

Regards,

Delgadoh

See Recover your iTunes library from your iPod or iOS device.

tt2

Delgadoh wrote:

You can either transfer the purchases to the new computer, or you can set the iPhone to manual mode and add the new songs while keeping the old. The article will go over how to do both options.

As far as I am aware an iPhone that has been associated with one library cannot be assoicated with a new one without iTunes wanting to erase and reload content from the local library. This normally means the loss of non-store purchases unless they are recovered first with third party tools. Setting the device to manual management on anything other than the "current" home library of the device will trigger the deletion of content.

tt2