DSL failed to connect ( Message ID NAD-3305): broadband communication down

In the past 6 days I encountered ongoing error messages " Arris NVG510 does not currently detect a DSL signal or is having problems connecting to Broadband Service." I have done every troubleshooting and diagnostic test ( too many to list here); yesterday I even reset the network adapter and the modem; did not fix anything.  The internet is now down every day for up to 24 hours and comes on out of the blue for about 5 hours. I know my modem is an old one that I purchased in 2013. I understand AT&T does no loner offer the option to buy one, but instead wants to rent you one for $ 10.00/month. I am hesitant to go that route as I don't have any clue what is causing that spotty connection. The landline phone also had some problems; I replaced the filter cable and the phone and internet worked for less than 1 day. Now the phone line is ok, but internet extremely intermittent. 

Does that indicate a problem with AT&T? I tried to open a service ticket the other day and received the message to order a new modem. Many readers with the same issues report that a new modem did not fix their problems. Whenever I checked my online account it never shows any problems.