When I install a new router it won't connect to the internet ?

You usually have to reboot the modem before it would work with another device.

The majority of cable/dsl modems bind to the network adapter's MAC address at boot time. What that means is if you disconnect the Cat5 cable from your computer and try to connect another device, it won't work until you reboot (unplug) the modem. In theory, you have to turn off the devices before (un)plugging network cables anyway ;)