I'm not familiar with Android tablets at all, but see if any of these steps help.
First, is the Verizon modem of the type "wireless hotspot" or "direct connect (usb, etc)?"
If it is a hotspot type device, are you sure the wireless is enabled on the tablet?
If it is a direct connect, is it securely connected?
You said you tried to connect by hard wire. When you do this, what happens if you try the connection type "DHCP?"
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