That's normally when the loading belt needs replacing, the very last part of loading is a bit tighter, so it gets so far but won't quite reach the end - there's a limit switch that it triggers when it gets there which tells it to kill the motor.
If you try and load a disc with it in pieces, you should be able to see the belt slipping or not - a good belt will probably stall the motor. While it's slipping try manually turning the target pulley, you usually find a turn or two will make it work.
I've got a small Sony DVD player that does the same, I got it as the customer bought a new one - but the belt was no longer available, and I've never bothered trying to find a suitable third party belt - but it works perfectly with the finger spinning trick