even when the plastic points are broken - there are normally ways to get it working again - the magic word is acetone.
its a tricky job - but i've done some plastic modeling jears ago with cell phone cases - today most car conditioning companies still use acetone to "repair" dashboards.
surely - some super glue can do this too - but thats always problematic inside electronic devices.
you can "glue" broken parts with minimum amounts of acetone and a few dissolved plastic pieces (anywhere scraped from the inside of the tv case) - this way the plastic stays plastic and you don't have to waste any thought for plastic welding, hot glue or something like that.
the acetone glue will be very strong - but you have to be fast - this way, fallen pieces can be repaired without bigger trouble