If the phone doesn't have a USB cable and doesn't work with Nokia PC connect software, the best bet is to copy your contact to the SIM and find a USB SIM reader and move the data that way.
Alternatively you might borrow a friend's phone which does connect to a computer and, having backed all his details onto his SIM, put your SIM in and transfer to PC that way. Best done with a friend's old phone or they'll curse if they have to reset everything, ringtones etc when you return it.
Sometimes we need to backup another contact information .I think if your contact list is not so long,you can copy it to the computer one by one.Of course ,it will cost you lots of time.Another idea is to chat QQ with your friend on your mobile phone,and send the contact list to your friend in front of a computer.And then invite her to send a copy to you by computers.
It will be better for you to get the backup.