Window Vista laptop gets a "local only" wifi connection from Verizon FIOS router. Can ping router but can't connect to the internet.

I ran into a heck of a time with a Windows Vista laptop and a new Verizon FIOS installation recently.  All other devices in the home could connect to the FIOS wireless network without any issue.  The Vista laptop would see the wifi network, it would accept the wifi password/key and it would show a solid connection in the system tray but the status of the connection would show "Local only", meaning it could not access the internet. This was certainly accurate because even though I could ping the router, I can't access anything on the internet.

After much troubleshooting, I figured out that I COULD access internet sites via their IP address, just not by their domain names. So this indicated that my DNS servers weren't working.  Everything was set on automatic but since it wasn't working, I changed my DNS settings to manual and I entered in two DNS servers used by Verizon FIOS:

4.2.2.1
4.2.2.2

The instructions on how to change these settings may vary slightly depending on your OS, but this method should work:

1. Hit the Start button and then type in "network connections" and hit enter.  
2. Now you should see your network device listed here - either Ethernet or wireless. Right-click it and hit Properties. 
3. Then click on TCP/IP v4 and hit Properties. 
4. On the bottom part of the window, select "Use the following DNS server addresses:" and enter those two addresses. Or you could try using two Google DNS servers if you like: 8.8.8.8 and 8.8.4.4.
5. Click Ok
6. It may require a reboot for those settings to kick in