I assume you are using firefox as your browser? Have you tried using IE or another browser? Is your system date and time correct?
Definitely mind boggling with 2 systems having the same issue with different hardware I would assume. I would say bring in a wireless laptop somehow and see if it can access those sights. If not, then I'm assuming its something with the router.
When I said reset it, that doesn't mean just unplugging and plugging it back in. You need to physically reset the router back to default settings. Usually there is a reset button on the back of the router.
Is your modem separate from the router or do you have one of the modem/router combo units?
Get a new router! Dlink is crap anyway.