Have you tried the suggestion here? http://forums.verizon.com/t5/High-Speed-Internet-DSL-and-Dial/Troubleshoot-and-Setup-High-speed-Internet-DSL-with-VZ-In-Home/td-p/211588
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?