PROBLEM FIXED
I finally contacted Apple Customer Care today, via the chat line. I don't have the Apple Care in longer, but they provided two options - 1) pay $19, and 2) Just installed iOS update. I selected the later. I restored the phone, as many of you have done here. The restore works fine, but once I restored the data to restore my old settings, the install process failed, a few times, but each time, we tried something else. I was felt that there was something in my backed up data that was causing a corrupt file which became part of the RESTORE process. I untimatley had to rebuild the phone back to 7.0.2, from the iCloud, where my contacts, calendars were stored. I had to give my phone a new name, and load my apps manually, which was a pain, but it worked, and now everything is RESOLVED.
I started the online chat at 1:27 pm today, and the woman, who was ever so patient, stayed online with me untile 5:45. Most of the time was waiting for the system that was hanging during the restore process. All my data accept for my personal settings were maintained, which was what was important to me. I think Apple Support Staff is AMAZING, and no one else comes close.
I like to tease my Android buddies, by saying, "Have you called Google?"