SLIDE the trim panel off

John Hibbert wrote an excellent verbal description of the trim removal process and posted it on Brickboard. Much of this narrative is his.

The only thing holding the complete trim to the door now are the four fragile plastic tabs at the top.  YOU MUST SUPPORT THE WEIGHT OF THE PANEL WITH YOUR HAND.  DO NOT PULL THE TOP OF THE PANEL AWAY FROM THE DOOR. The bottom of the panel will hang loose.   

Study the following images closely.  You cannot see this stuff until you have removed the panel.  Look at it here, understand how the fasteners slide down into the slots.  This understanding will help you to slide the panel up towards the glass without breaking the panel.

Here is the other part of the broken fastener.  This was the cause of the rattle.

Here is a new fastener, for reference.

Sorry for the poor focus, but you can see the keyhole shape of the slot.

Here is inside of the trim panel.  The black plastic is the fastener, attached to the trim panel. (Ignore the rugby boot)

Here's how the fastener attaches to the trim panel.

I placed a fastener in the slot so you could see how it fits.

You can now remove the trim panel by sliding the entire panel towards the glass.  Support the weight of the panel with your hand.  In fact it might help to press the panel in a bit along the top edge (along the glass) as this might loosen the fasteners from the slot.  A few light taps along the lower (cargo floor) side of the panel might help.

John recommended disconnecting the wire before removing the panel. I think you can remove the panel first, then deal with the wire.  I'm not comfortable with leaving the panel hanging whilst you fiddle with the connector.   There is enough slack in the wire to allow you to rest the far edge of the panel on the cargo area floor and keep this side close to the door panel.