@bullheaded WPS is about using physical button to establish wi-fi connection for the first time. It's not related.

You may look for settings like Security> ALG> SIP ALG, or Network> UPnP.

T-mobile Wi-Fi calling works for me but on a newer router with default settings.

Your phone should be connected to wi-fi first of course.

  @Rch11 Thanks for the clarification about WPS.   The phones' wifi capability settings are enabled, and the home displays show a wifi icon; the phones recognize and are connected to my router.  Looking in the Settings on the newer phone, purchased new yesterday, an AT&T Cingular Flex 2, I could find no reference to anything like  ALG> SIP ALG, Network> UPnP.  The router was purchased new last week, but I can not speak to how old this model product is.  The router is connected to a Hughes HT1100 Modem that is part of my Dish Network internet-by-satellite system, which has been in place for many years.  As the problem is identical with phones of different brands and operating systems, and my laptops have no trouble accessing the internet wirelessly through the router, the next course of action would appear to be to return the router to Staples.  When I shopped there for a router, I made specific mention to the salesperson that it must primarily be able to provide a wifi capability for cellphones, as I live in a total cellphone dead zone (-128dbm).  Meaningful accomplishment can sometimes not be achieved without a healthy dose of frustration.....

  @bullheaded 

ALG> SIP ALG, Network> UPnP would be in the router management page, like https://192.168.0.1/ or http://tplinkwifi.net/ - not phone.

Archer C54 is rather old indeed but should work for basic tasks like calling. That is all I know.

  @bullheaded 

I do not think that the AT&T Cingular Flex 2 supports wifi calling as I just reviewed the user manual and did  not see it. Check with att. 

  @ArcherC8 I visited the local AT&T store this AM because I was also unsure about the Cingular Flex 2's ability.  The store employee confirms that it does.  My username reflects my distrust of the obvious - the product packaging lists Bluetooth, Hotspot and WIFI Support among it's attributes, but in light of it's failure to connect calls, an in-person visit was warranted.

  @Rch11 Thanks for the tip on where to find the ALG and UPnP settings.  When I visit Staples tomorrow I will be sure to bring these topics up for discussion.

  @bullheaded You should try some other non public (public ones may block it) wi-fi network with mobile connection disabled to see if wi-fi calling works with your mobile plan, if you are new to it.

E.g. many mobile providers or MVNOs support it, but require to enable it explicitly in mobile account settings and set up E911 address.

There is zero chance some Staples sales person will know anything about it.