Howdy!,
I have Basic DSL Service with AT&T.
They have been sending me letters about their Advanced Digital Network.
From what I can guess by what I've read is they may be putting Fiber Optic lines in my area.
The letters mention a Wi-Fi gateway and to me it sounds like the Telephone Company is changing their DSL Internet Service to a Broadband Modem/Router (as in Cable TV) which I learned is like using a Party Line instead of
having the Twisted Pair Private Line I now have with their DSL/Telephone
As I asked above, Can the Wi-Fi part of a Broadband Router be turned OFF
by me?   Thanks for reading.
 
A little late with an answer but here is my two cents worth. First DO NOT
give the land line as you found out the cable/Fiber phones die with some
power outages. And also do not think you can always use a cellphone as
besides dying in some power outages the computer controlled system can be
taken over by first responders and you could get "No Connection' in major disasters
On the wireless modem router as far as I know you cannot turn off the
WiFi portion. You just set up a secure password and set up wifi security
and just do not sue it
DO NOT believe AT&T about maybe getting Fiber if it is not in your area
already as th4y touted Fiber coming to my area some time back. After
several years of NO fiber even though they did put in some connection
boxes but never finished the project I gave up my wait and canceled their
wire DSL and went to Cox cable. 
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