Did you make sure that Web Service was turned on in the Server app before running the FileMaker install?
I'm assuming you mean toggling the button in the "Websites" pane in Server app to on (I'm not a server expert, so I just want to make double-sure). I tried deploying with this set to both on and off, and it worked in neither case (I suspected that the server's own Apache deployment might get in the way of FileMaker's attempted deployment, which is why I also tested with this set to off).
But out of curiosity: when you say "running install", do you mean doing an entire fresh install, or are you referring to the deployment process started within Admin Console? The only thing I haven't tried yet is a fresh uninstall/install of FMS...
The strange thing is that it used to work, but a restart seemed to cause it to malfunction.
So far I have only done one install. To make sure things were clean, I ran an uninstall of the FMS12 first. I then removed the left-behind log file since that can cause problems. Then I reinstalled FMS13. Of course I first made sure I had screen shots of my Admin console settings and I had exported the schedules and groups so I could set things back up the same.
I am running on 10.9. with the Server app (I know this is theoretically not yet supported, but it worked before...).
Unfortunately, FMS 13 doesn't integrate with an existing apache installation the way it did before. I suspect that your specific problem is due to the fact that the Deployment Assistant couldn't kill the running httpd processes, so it couldn't listen on port 80.
If you reinstall or redeploy FMS13, I'd recommend turing off Server's web service's first.
You'll find that FMS has its own apache installation at:
...and that you can't use OS X's Server web service at the same time (at least not on 80/443). This is really very unfortunate. Its being discussed in some other threads, such as: