Strange connection issues

I have an new C3000 100NAS  Firmware 1.01.11.  This replaced an identical router that had burnt out.  None of my iPads or iPhones will connect consistently to it.  They work every once in a while.  I have a vizo TV hooked up to the router via the wire, and it works fine.  I have another TV hooked up via the wifi and it works fine.  My windows computers work fine.  My xBox one does not work.  I can't hook it up via the wifi or the via a wired connection.  It gives an error message about DNS.

Everything looks like it should work on my iOS devices.  I have a signal.  I can connect (it seems) and when I look on my setings, I the IP address, Subnet mask, router and DNS all have values displayed.  My speed is sometimes OK (upload speeds ranging from 5 to 35 MBS) and sometimes non existent (0.01 MBS)  My ping is almost always very good, 8 or 10 ms, even when the speed is near zero.

I have called my ISP provided once, and they reset my modem from their end.  It worked fine for a few hours after they did this.  

I have tried powering off all devices and restarting everything on my network  That made no difference. 

The inconsistent performance across different types of devices is what has me confused.

The old router did not display these symptoms.  It would quit working completely and needed to be powered on and off several times per day.  When it quit working, only the devices connected via a wire worked.   All wireless devices did not, so I am sure the new router has a different issue.