iPhone error (2001)

I've just taken delivery of my new iPhone - all fantastic - had it up and running etc., and then I went to upload the latest update...and all has gone a bit bad...

This is the process I have been through so far:

1. Went to download update. Failed - error (2001).
2. Rang Apple
3. Created new user
4. Downloaded update successfully with no problems
5. Went back to regular user
6. Unplugged/replugged in iPhone to USB - get message "iTunes has detected an iPhone in recovery mode. You must restore this iPhone before it can be used with iTunes.
7. On the screen is consistently an image of a USB with arrow pointing to iTunes icon.
8. Unplug USB. Hold Home button and replug USB...get same message as above.
9. Choose Restore and Update (again - tho it did it successfully when I used new user account).
10. "The iPhone could not be restored. An unknown error occurred (2001).
11. Click OK - disconnects iPhone from iTunes.

Any advice?! I've got a case ref. with Apple so I'm going to ring them back too.

Thanks, Mel