CM500V and Synology RT2600ac: no internet

do you have a screen snip of your modem connections page as well?

So it works fine if you have a pc connected to the modem but if you connect the router tot he modem, it doesn't work? 

Usually we tell people if a direct connection works great, then you move on to the next device in line that could be causing issues. 

Have you tried replacing cables? 

Are you booting up in the proper sequence?

shut both devices off, boot up modem and give it a couple minutes, then booting up the router? 

In terms of checking your router, you'd probably want to ask on the Synology forum as that'd be their device.