Tried updating my iPhone to 8.3 yesterday. iPhone 5 now dead and unresponsive even if I plug into iTunes. Help!

Yesterday I tried upgrading my iPhone 5 to 8.3. Phone told me not enough storage so deleted some stuff and proceeded. It then had a circle going round and round and wouldn't do the upgrade. I had to restart my phone a couple of times but it seemed ok. This morning went out with it 100% charged. Noticed it wasn't getting any phone signal so attempted a restart. Since then all i get is the apple logo on a black screen for a few seconds then it goes and nothing else happens.

I have tried leaving the phone in. Tried turning the volume switch on and off then restarting. Tried plugging it in to computer to do a recovery from iTunes but it's not showing on iTunes (which is up to date). Does this mean it's completely dead? It's infuriating as I'm a month away from a free upgrade from O2!!!

Any ideas gratefully received.