QuickBooks is supposed to start in the background, when you turn on your PC. The solution is to start QuickBooks by either opening QuickBooks or enable the service.
Right click the task bar. Click task manager. Under start-up, ensure QuickBooks is enabled. Here is an example.
In older versions of QuickBooks, there is a checkbox under general preferences called 'Keep QuickBooks running' that should be unchecked. If you open your task manager, you should see QuickBooks as a process. You can try logging into QuickBooks as admin and opening the company file. Minimize QuickBooks.
If problems persist, log into QuickBooks as admin and open your company file. Run the web connector.