If the subnets are 192.168.1.1 and 192.168.2.1 [for example] it is likely a firewall in a router or server is blocking Filemaker ports.
Thanks David. The difference is also in the second place of the ip address because the company's network is segmented more, i.e. the ip addresses of the client and server are A:X1:Y1:Z1 and A:X2:Y2:Z2 (only the first number is the same).
We've tried turning off the firewall on both the client and the server computers, but that didn't help. There may be others along the way, especially the routers, that is a great suggestion. Are the Filemaker ports:
TCP Port 5003
UDP Port 5003
or are there any others that need to be opened up?
Besides port 5003, have ports 16008 through 16018 also open. You may also want to review Knowledge Base Article #6427: