Solution
This error can appear when the Application Web Service, or one of its dependencies, is not running correctly. You can follow the next steps to try to fix this issue:
1. Go to the Windows Services, and check the status of the NI services, specifically the Application Web Server:
2. Right-click the NI Application Web Server entry and select Properties>>Dependencies.
3. Check the status of the dependencies in the Windows Services and make sure all of them are running correctly, otherwise you can get "The dependecy service or group failed to start" error when trying to start the NI Application Web Server service.
4. If the Application Web Server or any of its dependencies is not running, try right-clicking the affected service and select Start.
- If this fails check the Windows Event Logs by pressing <Windows+R>, typing eventvwr and clicking OK, then go to Windows Logs>>Application. The logs here can provide further information on why a particular service is not able to start successfully. For example, the Event Logs can point to an error in one of the configuration files for the problematic service:

In this case, correcting the mentioned line enables the System Web Server to start correctly, which in turns will allow the Application Web Server to start successfully.
5. Once the Application Web Server and its dependencies are running, try deploying the web service again.