Nathan,
I assume that you’re pinging using the ping command at the command line. Do you have a SIM inserted and cellular configured with the correct APN? For the Ethernet connection: Which version of AEP are you using, and are you configuring your Ethernet interface as a WAN with a default route?
In order to reach the Internet through the Ethernet interface you will need to configure the Ethernet interface as WAN with a default route to a router that can route to the Internet. You will also need to configure WAN access to the UI and SSH in order to be able to access the GUI through the Ethernet interface once it is configured as a WAN. To do that you would go to Administration->Access Configuration in the UI and select “Via WAN” for both HTTPS and SSH access.
In the upcoming AEP 1.1 release the Initial Setup Wizard and Network Interfaces pages in the UI have been enhanced to make this process much easier.
Jeff Hatch