Hi
You may have to sing wearing earphones. Without more sophisticated equipment I can't see how you can do it.
You can try this however:...
Place your backing track on Audio track 1 and play it through earphones from your PC. You should add a further audio clip ...an intro cue of some sort for a few seconds duration at the start of the audio track before your backing clip starts.
Using the VP Video capture screen, set up the camera to give you a suitable image with sound (use a mike on the IN socket of your PC if necessary, check you can make a video clip with sound and then close the Video capture window. (You don't need this test video so dump it)
Put in your earphones and start the audio track playing FIRST and THEN during the intro you added, open the video capture window again. You should now be able to hear the backing track for you to sing to through the earphones. The intro cue you added is just to allow you enough time to open the camera recording screen and press the red button. Start singing when your backing track starts.
The camera should then record only your voice with your image whilst you are singing but you will be hearing the backing track via the earphones. Small earphones could be almost unnoticable. I think this is what you are after. Your clip which will appear in the media list window when you stop recording should then be just of you singing. The backing track will not be heard.
NOTE: If you open the video recording window first you won't be able to open the audio track.
Nat