Need Sync/backup help

[barbie]

OK, not sure if this is the right place but here it goes.

I had to send in my laptop (windows xp) for repairs and they wiped it clean. (I didn't back it up, my fault I know) that's another story. So, in the meantime, I bought a new desktop because I needed a backup computer (my old desktop died) and I was frustrated with hp repair services (it's been over a month since I sent it in, again another story )
My iphone decided to crash on me. I was "stuck" in phone mode. I could move freely between voicemail, contacts, etc. but I couldn't go to the homescreen or turn off the iphone. I dowloaded itunes into my new computer and told it to backup the phone and restore it. It did this except it didn't put back any of my apps. I have previously had to restore my iphone with a computer I had never synced to before and it didn't do this. I talked to apple and they gave me credit for my songs I lost (I only had 10) and I've downloaded all my apps into itunes. I'm scared to sync it again because it pops up with a message saying its synced with another computer. I don't want to lose my contacts. I need confirmation that it won't lose my contacts OR preferrably I'd like to find out how to save them to my computer in a text file I can read on the screen.