Crackling sound when changing volume is actually pretty common for cheap analog volume control knobs. Turn the power off and turn the knob back and forth a few times and it might go away or at least lessen.
No sound for hours is not a good sign, but:
- Do you have the PC audio muted? (Look down at the system tray)
- Do you have the audio in whatever you were using like YouTube muted?
- Did you plug the Logitech into the right connector on the PC? The mic IN won't work
What happens when you run Windows or Logitech's audio test / speaker test?