Thank you for the post.
A few additional questions to assist us in narrowing this down:
1. What is the FileMaker Server 13 computer's operating system?
2. Is the FileMaker Server 13 version 2?
3. What does "http://localhost/" load from a browser on the server?
4. What browser(s) were used for testing?
I am having similar problems. Under Activity>>Web Publishing Engine it shows that the "FileMaker WebDirect is disabled" but when I click the little sprocket button to the right of that it takes me over to the Web Publishing>>FileMaker WebDirect tab and the check is definitely there to say "Enable FileMaker WebDirect." Also, today I noticed that there was not a check beside the "Automatically start Web Publishing Engine" so I put that there. I restarted my server but the Web Publishing Engine was turned off at first anyway.
To respond to your four questions,
1. Windows Server 2008
2. Admin Console version: 13.0v2 x64 (04-20-2014)
3. Going to http://localhost/ on a browser on the server goes to a blank (all white - absolutely nothing) web page. This is what I see when I go to the URL of the http://<IP Address>/fmi/webd web addresses as well.
4. Originally I was using Firefox. But when you said that I tried Chrome and IE as well and got the same results.
Is it possible that there is a commandline prompt that I need to use at on the server similar to what you have to do in that rare occasion when the scripting engine gets stopped in FM Server 12?