You receive an error that the "Background service is not running." This error can occur when the PDQ Console attempts to connect to the background service, but the background service is not running.
Ensure that the background service is running. You can check the status of the background service by going to File > Preferences > Background Service (or press Ctrl+comma > Background Service) or through services.msc.
You can also start the service from an elevated command prompt:
sc start pdqdeploy
sc start pdqinventory