Port 591 is the recommended port for Filemaker. You might have to open the port on your firewall / antivirus software.
OS - Win or Mac and version?
Multiple Firewalls running? (Norton and McAfee are notorious)
Database location? C: drive? Desktop? Documents folder?
Get Info or Properties on DB file - read only?
Your user has admin rights?
Do you have other internet utilities or applications running?
Does your ISP (internet service provider) allow this? (some don't)
Changing the port number often requires a restart.
IWP threads on these forums - https://www.google.com/search?q=IWP+site%3Aforums.filemaker.com
IWP Limitations threads on these forums - https://www.google.com/search?q=IWP+limitations+site%3Aforums.filemaker.com
A post about IP Addresses and Ports http://forums.filemaker.com/posts/1dcab8c50e?commentId=21392#21392
StepbyStep for Mac very specific http://forums.filemaker.com/posts/1dcab8c50e?commentId=21403#21403
My database is hosted on Filemaker server 11 by oditech.com
I use FMP 11 on the Mac OSX platform.
Since you have a company hosting your database for you, I'd contact them for tech support on this as there could be a setting they need to change on their end to make this work for you.