Can you pull a backup off of an iPhone3G in "connect to itunes mode"?

Ok here is my situation, recently my harddrive failed on my laptop and it got replaced. I had not yet synced my iPhone with it out of losing all my music. Now today my iphone froze up and i hit the home & wake/sleep button to force restart it. Now it is stuck on the apple logo and sometimes it will come up a loading circle and stop about half way through a rotation. I have force restarted it multiple times. I also have been able to get it into “restore mode” easily. My question is: Is there anyway i could possibly pull a backup off of my iPhone in “restore mode” The worst thing is because my HDD got replaced in my computer i will lose most of my contacts since i’ve gotten to college and thats alot of ppl to try to get numbers back off of, I’m not so worried about the music as i am my Contacts. If there is anything or any ideas you have please put them on here. I’m fairly skilled in these things typically but this one hit me by surprise.