Itunes won't connect iphone 4s?

My mum got the new iphone for Christmas so I got her 4S to replace my ancient iphone 4.

I connected her 4s to her computer and restored it to factory settings. But I can't get it to register on my computer when I plug it in?
The little message pops up asking if I'd like to trust the computer, I click "Trust" on the iphone and that's where it ends.
I've rebooted the computer, the iphone and Apple mobile device support. I've updated the iphone and itunes to the latest software.

Still nothing. Any ideas?

Try taking it to your carrier, it shouldn't be doing that, you could try Apple Forums. At www.apple.com

ONLY DO THIS AS A LAST RESORT! This will put you into DFU mode and will force you to restore what you do is when the phone is plugged into the computer turn off the phone hold down the power button for 3 sec then while still holding the power button hold the home button for 10 sec and after that release the power button and after that you computer will say it dected a phone in recovery mode ( same as DFU mode ) click restore and you should be done. If something goes wrong and it won't turn on after hat to to YouTube and look up how to unbrick your iPhone, put your phone in DDU mode ( I would go to video that way you see how to do it, and what to do if iPhone e won't turn on. Everything is reversible if you know what to do. Hope this helps

Make sure of using iTunes 11.0 or newer because 4 & 4s don't work on 10 and after clicking trust this computer then open iTunes, and after some time your iphone should be available