Follow-up. Got the replacement in less than 24 hrs. from my phone call to AT&T (their customer service is much improved).
I backed up the old phone (finally successful) by using Kies. I then tried out the new phone which seemed initially at least to be working properly. I then reset the old phone back to factory default. When I went back on Kies to update the new phone to the old phone's personaliztion, it FAILED me. Despite an apparently successful back-up having been done, Kies "due to limitations" was unable to copy my music, notes and contacts to the new one. I was able to get my music without the playlists by name transfered to the replacement phone. Pictures came via my external storage on my sD card. The other files, etc. had to be done by multiple means: AirDroid, and manually. Unlike the convenience and utility of iTunes, it took me many hours!!
Now....when I'm back to work at the multiple places that my usual day takes me to, I'll see if the WiFi is any better. Just as the phone it replaced, my home router and WiFi have not been a problem, but it is not where I need WiFi. Phone calls with this phone are just fine as is the Bluetooth.
Stay tuned for follow-up on the S4's many WiFi issues. If this phone mirrors the problems I've been having, I'll seriously consider buying my way out of my AT&T contract and switching both carriers and phones to Verizon and the iPhone.