No Network Access on Macbook air either through Wi-Fi or tethered to a phone I cannot connect to the Internet on My Mid 2013 MBA, running 10.11.3 either through Wi-Fi connected to my router, or tethered to my iPhone via USB or Bluetooth . Rebooting the machine has not solved anything.

I cannot ping any  external IP, I can ping other devices on the network.

All other devices in the house (Various ipads, iphones, windows PC's, NAS Box, Raspberry Pi's etc) all connect fine through the same router. Resetting the router hasn't helped either.
I've had similar problems with macbooks. I've found that going into "Network Preferences" / "Location" / "Edit Location" and creating a new location can work.

Here's another option:
set your IP manually to an IP the router will accept, instead of by DHCP. If your other devices connect at 192.168.1.25, for example, configure yours to 192.168.26 (keep it close to other IPs in case your router is set to limit to specific IPs). Apply your changes and try connecting.