depending on which upgrade they installed, it may take a few tries to resolve this.
First, how do you normally back up this iPhone?
Ok, first try the following;
Disconnect the device from it's cord, if plugged in.
Press and hold your Sleep/Wake button (on the top) and Home button (on the front) together for around 10 seconds.
When the Apple logo appears, release both buttons.
The next thing you should see after the Apple logo is the home screen a few minutes later.
If the above does not work, let me know and we will move on to the next option.