Ahh, just use a different ip. Instead using the url, use the local ip of the computer since you're in the same network already. For example if the computer's IP is 192.168.0.101 you would use that instead of myip.dyndns.org for example.

if you're saying that the computer is not a static ip, then you can set it static by using a rule in your dhcp setup on the router. In this way the DHCP server give the same IP to the computer without an expiration on lease time, effectivly making the IP permenent and static.

2d