plug it into a different computer, one that you don't use to sync, and make it manually sync all of your info.
next I think you would use an app called senuti to get your mp3's off your phone, and other info, calendar, contacts, etc. I think you can just sync and it'll take them off your phone and put them on your computer.
I'd quadruple check everything I told you first so you can make sure it'll all work.
and next time go buy a 50$ external hard disk and back up your important data.