The DNS server isn't responding

I have a dell xps L502X with windows 8. My network adapter was replaced last month. My DHCP is enabled. My DNS Server reads 192.168.1.1 and it's a home/cable/DSL connection so from what I've read that's right. I've set my IPv4 and IPv6 to automatically detect the DNS server and IP address to use. I've tried to reconfigure the computer to the wireless router, but when I go to set up a new network no networks pop up even though many networks pop up for me to connect to on the right of my screen. All of my other devices are connected and working fine. That was the background and what I've tried to fix for my problem. When I try to connect to my home network it says it's a limited connection meaning I have no Internet access. When I run the trouble shooter for the network, Internet connections, and network adapter the only one that has an issue is the network one and the issue is that the DNS server isn't responding. Please help I've tried everything I could find to fix it.