Asus has some routers that have issues, and certainly Sonos doesn’t work with WiFi extenders. You may want to try wiring the amp directly to the root of your system to see if it works then. Do not wire it to the WiFi extender…many of them split the network into two subnets that Sonos doesn’t cross. 
Here is the new router - installation instructions FAQ, there may be information that can help you. 

Power down the new Amp, reboot the router, power the Amp back up.

Any DNS filtering or VPN on your gear? Disable and try again.

Make sure the router is set to something Sonos accepts.

Amp is “n” only on 5 GHz and ‘b/g’ on 2.4 GHz.

https://support.sonos.com/en-us/article/supported-wifi-modes-and-security-standards-for-sonos-products

I’m having the same issue with my first Sonos amp. I was on the phone with them for 2 hours yesterday and they couldn’t figure it out. The Port connected perfectly but the amp only connects wired Ethernet. Now that you posted the link to wifi modes, if I’m reading the chart correctly, Amp does NOT connect via 5ghz at all. It’s only listed as 2.4ghz on n. If that is so, that is my problem (not using 2.4ghz radio atm). The tech support rep said Amp was 5ghz compatible too, but as we know they aren’t always correct.  I’ll try turning on the 2.4ghz radio tomorrow when I get a chance to see if that fixes the issue

Yep, I read that wrong, I missed the 2.4 / 5 GHz split in the text, the Amp is able to do N buy only on 2.4.

Way down the page under Power and Connectivity.

https://www.sonos.com/en-us/shop/amp?sonos=native

Thanks for all the replies.  No luck yet.  I powered everything down and back up.  I modified my Asus router to disable Airtime Fairness.  

I then modified to “n only” on 2.4 GHz.

Still no luck after both changes.  

What else can I try?  I wish i could attach a picture/screenshot of my router settings for feedback. 

The amp just doesn’t want to connect to my WiFi that I use everyday on my phone and other devices.

I’d call Sonos Support directly to discuss it.

Just an addition: all Sonos home theater devices (Ray, Arc, Beam and Amp) use the 5Ghz part of their wifi card only for the dedicated link to the Sub and surrounds. Even when you have no Sub or surrounds, they cannot be connected via 5Ghz.

A fact that escaped the rep trying to help me connect my amp evidently.

For future readers of this post I can confirm that Amp only connects to network on 2.4ghz bands, which is clear in the documentation if you read it. I turned on the 2.4ghz radio for the WiFi network that my Sonos is on, unplugged the Ethernet cable from my switch to the Amp and it connected wirelessly automatically as it should. The Sonos rep assured me the Amp was 5ghz capable and was unable to figure out why it would not see the network wirelessly. I still haven’t gotten a call back from them after submitting the last diagnostic. Glad I pursued this on my own and came across the link to the Wi-Fi specs. Thank you.

Hey Guys!  I’m the original poster and just thought i would give resolution to what my issue was.  It’s such a dumb oversight.  I never moved my Sonos Boost connection from my old router to my new router.  It was still plugged into the old router.  How dumb!  I was so focused on the App and getting my wifi connected that I never took the time to move my Boost over.  Funny how it is so often a simple fix that is over looked.  Thanks everyone for your help and ideas!