I have just set up my XE5300 with 3 routers, and upgraded firmware on all 3.  System topology looks like the diagram below except there's also a desktop computer connected directly to the base Deco with an Ethernet cable.

Issue I had was - WiFi was working fine, and wireless devices had Internet, but the desktop computer had no Internet connection.  Devices connected to the switch were working though.

After finding other mentions of the same problem, I started some troubleshooting:

1.  rebooting all 3 Decos did not help

2.  changing the Ethernet cable connecting the base Deco to desktop computer did not help

3.  was able to obtain Internet connecting a laptop to a satellite Deco's Ethernet port (port #1, the top-most port)

On the base Deco, I noticed that I had connected it to the modem via LAN port #3, the bottom port.  The desktop computer cable was plugged into port #1, and the switch cable into port #2.  On a whim, I pulled the cable from the modem out of port #3 and plugged it into port #1 (leaving the desktop computer Ethernet cable temporarily disconnected).

The Deco status lights went solid red, so I pulled the power cord out of the base Deco for 20 seconds and then powered it back up.  After a short time, the status lights all returned to solid green and the WiFi was working again.  I then plugged the desktop computer's Ethernet cable into the base unit LAN port #3, and it connected to the network!!

So it appears that the base Deco must connect to the modem via LAN port #1, but the instructions do not say this (nor are the ports labeled in a way that makes it obvious).