|If 192.168.1.1 works, 10.0.0.1 never will and if 10.0.0.1 works 192.168.1.1 wont.|
Both ar private IP addresses which means they are always on a local area network and behind a router. The two IPs cannot exist on the same network.
All the ping 192.168.1.1. tells you is that you are connected to your router. You need to check the connection from your router to the Internet.