Have you checked for any errors within the logs of the SEPM's Apache server? These are usually found in "%ProgramFiles%\Symantec\Symantec Endpoint Protection Manager\apache\logs"
The odd thing in your situation is that the SEPM is working. This is usually not possible without the Webserver service running as well. Can you confirm that the "Symantec Endpoint Protection Manager" service is defintiely started?
The only thing I can think of that might bring about this situation is if someone has deliberately started up the httpd.exe process in "%ProgramFiles%\Symantec\Symantec Endpoint Protection Manager\apache\bin" by other means. Doing so would casue the process to bind to the SEPM's client communication port (8014 by default), and thus prevent the "Symantec Endpoint Protection Manager Webserver" service from starting.
You could try to verify this by running a netstat on the SEPM and see if anything is listening on 8014. I'd also recommend using the -o switch with netstat so you can grab the PID and check task manager to find out under which context this process might be running (i.e. SYSTEM, or a specific user...)