You might want to use a third-party application such as CopyTrans Contacts to effectuate the contact transfer to your computer:

http://www.copytrans.net/iphone-contacts.php

I used the app to transfer contacts from a broken iPod Touch to a PC. It should also work for your iPhone.

The method below does not require iTunes or an online connection:

1. Run copytrans contacts and connect your iPhone. Once the contacts appear drag them to your computer's Desktop or to, say, your Contacts folder

2. You will have the entries saved in vCard format on your computer.