PRTG Traffic Grapher currently operates on a dual mode, namely as a GUI or as a service. Once the GUI is started, the service is stopped - and vice-versa.
In the unlikely event that the PRTG service ceases to start when shutting down the GUI, it is always sound to update to the latest PRTG release, seeing as each update / upgrade generally increases PRTG's stability.
If this does not solve the problem, please try the following:
The service should not start (check with Task Manager). If so,
The service should now start in a timely fashion.
Basically, this procedure quickly uninstalls / reinstalls the service, guaranteeing for proper operation. This process also assists in the event of the web server not operating properly while running the software as a service.
Important note: In order for the service to function properly, the service needs to be installed and executed from within a system account.