My wife had the same garage door problem...but without as much damage. My solution was a plain motion detector light that comes on when you walk into the garage. The light is aimed at the garage door ...it brightly illuminates the white garage door, so she notices the door is still closed.

 

Excellent tip. Thank you very much.

 

Here is a tip: Now that you're parking inside the garage, do NOT use the buttons inside the car to open the garage door prior to backing out. It's inevetible that someone will forget to push the open button before reversing, ka-boom, and now you need a new garage door, or at least an expensive repair.
We always use the button on the garage wall to open and close the garage door when the car is inside. Hope this helps.

 

Ray, that's a great tip for more reasons than the obvious. When I walk out of the kitchen into the garage I go ahead and punch the door open. In the walk behind & around I'm also checking there is nothing left behind the car prior to putting it in Reverse.