I held down the phone's right hand side power button and the front home button at the same time, for about ten seconds. Then the Apple logo came back on the screen, and after a few minutes I was able to redo the set up process. I had tried that previously without success, but I hadn't held the two buttons down for long enough - it took about 10 seconds before the phone eventually responded.
Good luck, I know how frustrating problems like this can be!