When get a new computer, your iTunes of cause is needed to reinstalled on it. Consequently, your iTunes library is empty and will wipe out your iPhone library then leave you no library anywhere. So if you want to tansfer files from from iPhone to New Computer, you'd better turn to some way else. You can try some third-party transfer software, like Cucusoft iPhone to Computer Transfer which is powerful in iPhone backup software.
The full version of iPad/iPhone to Computer Transfer can:
Recover, backup, restore iPhone files
Transfer files between iPods, iPads and iPhones
Transfer iPhone songs, videos, photo, podcast playlis from your iPhone (any model) back to your pc/itunes.
Guide: How to transfer files from iPhone to new computer?
Step 1: Connect iPhone to new computer and Launch iPhone to Computer transfer. Then the program will search the device automatically.
Step 2: Select files to transfer from iPhone to new computer, then Click the Export button.
Step 3: After you clicking the Export button, the following window will pop up, you can choose transferring to computer or iTunes directly. You can set the output folder at Advanced->Options before transferring...
Step 4: When the transferring finished, the following window will pop up. It shows that how many files have been done. You can click the OK button to view the files transferred from iPhone to new computer.
Ok, iPhone to a new computer transfer has been done, just enjoy it.
For iPod User: Transfer iPod to a New Computer