iPhone restore without SIM

When I upgraded my iPhone, I kept my old iPhone 4 to use as an iPod touch. It was getting so full of rubbish that I decided to wipe it and start again so I did a restore. I didn't realise that I needed a SIM card to do this and now my phone is refusing to reactivate. When I plug it in to iTunes, I am not offered any options of using previous backups. I haven't kept my old SIM and don't have one that will fit into my iPhone.

Is there any way I can bring my old iPhone back to life without a SIM card?