Sarah, that last picture should definitely not happen. What address is your router set to? It must not be set to 192.168.0.1 as that is the address of the modem. If you still have the error when plugged directly into the modem and go here http://192.168.0.1/ then there has to a problem with your computer or the HughesNet modem. If you see the System Control Center at the link then at least that portion of things are good.
Some antivirus programs run you through their DNS server like the Comodo antivirus and it will cause you to get the DNS error on every page, try uninstalling your Antivirus temporally and see if you can browse that way.
Charles Scott, Champion everything is configured correctly, hometec checked that to! The router I have is a Belkin N300 XR Wi-Fi N Router...Also when I completely unplug router It does the same thing..
Open an elevated command prompt and type in "nslookup" with out the quotes and press enter, type the information out here, you should get a Default Server and an Address. You should be getting something other than 192.168.0.1 if your using a router.