If once the tape goes in you hear a slight whining noise before it's rejected it's possible the rubber band on the motor is slipping.
If you unplug the video and remove the bottom panel you'll see the motor and rubber band running to some wheels. Try removing the band and cleaning any grease from it, and also cleaning any grease from the wheels.
This may make it grip better and make the mechanisim work properly. If this doesn't work or only slightly improves it, the band may have stretched so you need to try and replace it.
Mac, September 2007
