You have to set up the router of the host network for the correct port-forwarding. You have to forward traffic on port 591 to the PC that is hosting the file. The PCs outside the building's network also have to know the IP address of that hosting router.
So the route from outside should look like:
Remote browser links to hosting router, eg: http://123.456.789.123:591
Port forwarding on the hosting router forwards incoming traffic on port 591 to the hosting PC, eg:
Application Name: Filemaker IWP
Forward to: 192.168.0.254 (the IP address of the hosting PC)
If you can connect internally then it seems like you are correctly directing the browsers to, eg: 192.168.0.254, but you have not set up port forwarding on your router.
IP Addresses can be Static (constant) or Dynamic (may change randomly)
You have a dynamic IP address now (http://whatismyipaddress.com)
You have a router that allows the 3 or 4 computers to share that IP address with the outside world.
If you have the database running on one of your computers with sharing turned on
A request for your database from outside your local network will go the router. The router is not running the database and the request will fail (with or without error message). If you set the router to forward the request for that port to the computer running the database, outside computers will be able to access the database.
you can tell your router to forward port requests for Filemaker to that computer.
If your Internet IP address is 188.8.131.52 and the local computers' addresses are
Computer #1 192.168.0.2 (sharing the filemaker database)
Computer #2 192.168.0.3
Computer #3 192.168.0.4
You tell the router to forward Filemaker port requests to Computer #1 192.168.0.2
Another Post on the same Thread
FMP10 IWP Setup PDF
Testing your IWP setup.
If the database does not open, the IWP settings in Filemaker or the database are incorrect.
 At another computer on the same local network, open browser and enter http://hostlocalIPAddress:591/fmi/iwp
This should work if the first test works.
 At a computer on another network, open browser and enter http://hostlocalIPAddress:591/fmi/iwp
If the first two worked and this does not, the portforwarding on the router or firewall settings are incorrect.
I only ever forward 591, and it works for me. Does that not mean that all normal web-browsing traffic would be forwarded to the FM serving computer?
Port 80 is the default port, which is what HTTP traffic normally goes through. You may have reassigned it to 591 to resolve conflicts with your running web server or something. - John
I did this (from the IWP Guide), or rather "I suppose I always do this in order to avoid worrying about any other issues":
The TCP/IP address in the Instant Web Publishing dialog box determines where web browsers can find FileMaker Pro databases on the host computer. By default, FileMaker files are shared from port 80. If port 80 is already in use (by a web server or another application), consider changing TCP/IP Port Number to 591. FileMaker, Inc. has registered port number 591 with the Internet Assigned Numbers Authority (IANA) specifically for web publishing.
As it is a port assigned to FM, I don't quite understand why they wouldn't just go straight to the 'just use port 591, okay?' option. But the confession is in the statement : 'I don't understand'!
Because port 80 is the regularly used port for web traffic, and hence a lot better chance of it not being blocked in clients' routers trying to access the solution.