Have you tried the suggestion here? http://forums.verizon.com/t5/High-Speed-Internet-DSL-and-Dial/Troubleshoot-and-Setup-High-speed-Inte...
Was the D-Link router recently reset using the pinhole in the back, around the time this problem began? What are the IP addresses that are returning for the sites you are pinging?
When the D-Link was connected in that case, did the modem request to go through a setup wizard? For example, did the D-Link need to be set up with a username and password in order to actually connect? Does http://activatemydsl.verizon.com manage to load up when all other sites fail?
I wasn't there when she set up the DLink but (1) she was on the phone with VZ support and (2) I don't think I could have done pings and traceroutes unless she _some_ kind of connection.
Ping/Traceroute will simply fail when you try to run them if there is not a connection. If there is a connection, running these will at least give us an idea if the problem is with DNS, route, or something else such as a Walled Garden.
If you have to, have the D-Link modem reset by using the reset button found on the modem. Holding it for 20-30 seconds should cause the modem to reset to factory defaults. You will need to configure the modem again for service, and you can either see if an Activation screen appears, or you can give Verizon a call and have them help you set the modem up again. I am not familiar with how Verizon ships the D-Link modems to do a walk-through of the modem setup.