First, open up Outlook and make sure it's configured (has a user account set up, etc.), if it isn't already. Then, plug your iPhone into the computer, and open it up in iTunes. Under the Info tab, there is a subheading labeled Contacts. Check "Sync contacts with" and choose Outlook from the drop-down menu. Choose All Contacts, Apply the settings, and then sync your iPhone. The contacts should now be in Outlook, where you can export them to a flash drive or email them to yourself.
Also, there are free methods of unlocking your iPhone. Like Blackra1n.
http://www.blackra1n.com/Tutorial:
http://www.iclarified.com/entry/index.php?enid=5527
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