This is by far one of the most annoying problems I have encountered in the 10 years I have been working with computers. For some LAME reason if I brows the internet for a while, around 45min to an hour, I stop resolving websites. I can still get DNS's and pings but when go to, for example, google.com the page just sits there and loads and loads and loads. The only thing I have found to be a cure for this is to go to cmd prompt and type ipconfig /release /renew a couple times and do the repair when "limited or no connectivity" pops up.

I am at a loss! Out of the 7 computers on my network, my computer is the only one to do this and the firmware is up to date on my router.

Have you tried to flush the DNS? Not sure if it will work but worth a try. Run--Cmd--ipconfig/flushdns. It should say action complete. Restart computer and establish connection. Hope this works.