An iPhone is designed to be synced with only one computer at a time. If you want to change the computer that it's synced to copy the music etc. into its library and try the steps on this user tip : Syncing to a "New" Computer or replacing a "crashed" Hard Drive
Some of the steps on that page are slightly different now (it was written for a previous version of iTunes) :
5, File > Devices > Transfer Purchases
6, Reset Warnings is done via the bottom of the device's Summary tab in iTunes
7, File > Devices > Back Up (or Back Up Now on the device's Summary tab)
8, File > Devices > Restore From Backup (or Restore Backup on the device's Summary tab)