If your network prevents Filemaker peer to peer from working, it will probably prevent FMP Server from working also. They are essentially the same thing from a networking viewpoint.
Mac or Win? Version?
Can you give the IP addresses for the individual computers?
It is possible that a firewall is preventing communication on the 5009 port.
Can you share files between computers? Can you all print to a network printer?
Are you in the same office? Same building? Same city?
Do you have an IT department?
More info will help.
Mac, Running OSX Tiger. And I'm afraid I don't know the IP addresses for my colleagues in another town.
Because yes, I can share the file over FM Network fine with the other person in my office (and yes, we can print to the same network printer), but when my colleagues in the next town over try to access it, they can see an IP of some sort (so they can see it IS being hosted), but no list of available files associated with it. My colleagues who can't access the file have, in the past, been able to print to printers in our office, if the drivers have been installed on their machines. (I think - again with the lack of tech wizardry.)
Sounds like this is not just an easy "what do I need" question, but will require a heart-to-heart with our IT folks.