Buy a router and save yourself much hassle. But, Verizon uses PPOE or DHCP I believe so you would need your log in info if you are in PPOE areas. With a router, you could input the PPOE info to the router and not worry about it with anything else you hook up.
Besides that, turn off your XBOX, unplug the modem from the power, count to 10, plug it back in and when the lights are back to normal, power up the XBOX.