The URL provided by Web Publishing Settings is a local IP address (most likely) (192.168.0.3 or 10.0.0.4).
Local IP addresses are limited to computers connected to the same router (router that connects to the internet, usually not a secondary router,, depending on setup).
You IP address that the web uses is found by http://whatismyipaddress.com or many other such sites.
The URL you give some that is not on your network is that IP address with a port added (591 for instance)
Your router will have been set to forward that port request to the computer running the IWP access for the database.
See this Google "iwp david anders site:forums.filemaker.com"
The Computer Guy, Seattle
Found the problem ---
When I moved, the computer IPs changed (don't know why -- maybe connected them in a different order)..
Anyway --- had to change the local ip at the port forward.
I knew it had something to do with the move -- because everything was workig just fine before that.