While trying to upgrade my iPhone 3G from iOS 4 to iOS 4.0.1 i received an error 1603 from iTunes saying:
the process had failed to restore the iphone for an unknown error
Upon searching for the solution to this issue, there were many random things that fixed it for some people. However the way that helped me was pretty simple. Just RESTART your computer. That’s it.
Other people proposed like taking out sim card, using other sim port or other computer or turning off the apple mobile device service (which is logical to the restart process too).
Let me know if this was helpful in your situation and the error 1603 got fixed.