so, this means that traffic off the router, originating from the Shake Pi computer, is not making it to the outside. nor is the DNS server specified, 184.108.40.206 (google), is also inaccessible.
next test would logically be:
- can you plug a different computer into the same router, using an ethernet connection, and run the same commands from a command line?
if this isn’t possible, another test would be to plug the Shake Pi into a different router, one you know is connecting successfully to the internet-at-large, and run the same test commands there.
to be clear: there is no configuration on the Shake Pi that disallows connection to the internet through a router. these tests, so far, have confirmed that communications off the Pi are successful (original ping through the adapter returned the address of the adapter). not to mention that you are able to remotely log in to it, communications rarely are permissioned to happen only one-way.
without being there myself, i can’t absolutely say since i am not privy to your entire network’s setup and configuration details, but my conclusion at this point is that traffic off the router to the WAN is not working. on the other hand, this seems unlikely since i will also assume you have other devices using this same router to access the internet, and those other devices are not suffering this problem?
try the other tests, make certain to use a router you know accesses the internet okay, and let us know the outcome.