I went to turn on my phone and I got a black screen with a circle going round and round. The phone will not turn off and will not respond when pushing the home button. Can anyone help?
The steps to fix any iOS device that won't boot fully are the same and pretty easy to accomplish following Apple's support on how to restore a device.
Consider trying to make a backup or check if you have your data (programs, contacts, settings, photos) either synchronized or backed up before you restore - that irreversibly deletes everything you put on your phone as the first step of the restore:
At the bottom of that article are several that might need to be epxplored if the normal restore fails, up to and including calling for a hardware repair to an authorized (or unauthorized if you prefer) repair shop.