HTTP Server not accessible from intranet

We have a cable network and a few static IPs from the ISP. A server is connected to the cable modem (also as a router) and has a static IP assigned. An HTTP service is running on the server. Everything works pretty well, we can access the HTTP service from WAN. There is an office router plugged into the same cable modem. Devices connected to this router can access the internet without any issue, but they cannot access our HTTP service. However, they can successfully ping the server. What could be the problem here?

Question by hillin on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.