Why wont my purchases transfer?
To transfer your purchases from your iPhone to a computer, that is not authorized or sync previously, you will require a third party software such as podjammer or sharepod.
You can try this link as well:
These articles may also help you to copy files from one computer to other:
Mac: iTunes: How to copy music between authorized computers
Copying music between authorized computers with iTunes for Windows
However you need to authorize your new computer as well.
To authorize a computer, follow these steps for each of your accounts:
1) Open iTunes.
2) From the Store pull-down menu at the top, choose Authorize Computer.
3) Enter one of your account names and the password for the account.
4) Click Authorize.
Also note that you may only authorize up to five computers to play purchases made with one account.
You can also try this:
1. Create a custom playlist for your iPhone music library.
2. Click on the "Music" tab and you'll see that you can select "sync playlist". Do that, then select the new iPhone sync playlist you've created.
3. Set things up just as I have shown and that's all there is to it. Now click "Sync" in iTunes and it'll synchronize your playlist with the iPhone music library and next time you click on that ole' "iPod" button on the iPhone, your selections from you music library will be present.
Besides what mentioned above, you can follow this article about How to transfer music from iPhone to iTunes on PC,which can help you to figure out how to transfer songs from iPhone 4 to iTunes easily and fast.
Have a good luck.