ping: cannot resolve google.com: Host name lookup failure
When you put a host (a computer) behind a router, you might suddenly get a "host name lookup failure" even though your network was working a moment ago. You are pretty sure your network is up, your nameserver is working, and you can usually fix it by restarting the host.
You can fix this without restarting a host. The problem is very likely that your host does not use your new router as a default gateway. you simply need to add that as your default route using:
route add default 192.168.1.1
assuming 192.168.1.1 is the router.
you might want to flush the route using route flush
Read the interesting FreeBSD handbook here
check your routing tables with
renew your dhcp lease with
re-enable your (network) interface with
ifconfig interface up
ifconfig interface down
check your nameserver at