this is a lot, but maybe it will help someone.
OK, I called AT&T and the rep I chatted with was helpful. We agreed that it seemed to be a device issue. So I worked with my device for over 2 hours now. I have McAfee instsalled (has been for over a year and the device connected for 6 months - the problem has been for the past month - at least) on the SAMSUNG phone and what I did was to change the McAfee setting on the device limit to a higher number (it was on 2GB and I changed it to 5GB - my verizon plan only has 4GB) When I did this, I got the wifi icon at top of the phone, on the notification bar. Dunno if this change itself solved the issue or if something else changed somewhere else (like maybewith the ATT router/modem); cause I then changed it back to 2GB but the wifi icon stayed. Also location is off and Auto Network Switch is UNCHECKED and "Keep Wi-Fi on during sleep" is set to "Always" and I turned Powersaving mode off, but just turned it back on. Also, as I was "playing" I turned off the following: Samsung Link, Samsung Print Service Plugin, Sansung Push Service, ans S Suggest as I remember playing with and updating this trhu google play when the wifi initially disappeared. Also McAfee was not happy with NFL Mobile app (said it had too much control in my phone) - I don't even understand football, so I know I did not install it. So I turned this off (Force Stop) and disabled it but can't uninstall it - with McAfee nor with the Samsung phone.
So the wifi icon appears, but if it disappears again I will contact this forum. But, for now I have wi-fi.

Will see how long it lasts. For those with this problem, there is also good advice (a variety of possible fixes) at this address for Android Central (forums.androidcentral.com):
http://forums.androidcentral.com/sa...cured-but-won-t-connect-no-matter-what-4.html
Just a note, although I can now connect, I CANNOT "forget" my home network; no matter what I do. That's seems a bit strange.
Hope this helps someone else. Am not working right now so really need this to be working as part of my job search.
Community groups are GREAT !!!