Quite possibly - also if the EOS switch is not working - the coil stays in high-power mode and can burn out...

Take a photo with your phone and post it here - (press the + Additional Options button under the edit box)

Do you own a multimeter? Know roughly how to drive it?

I'm trying to work out if the switch block has fallen to bits - or the flipper link is broken?

100% correct - the flipper would become weak after a game or two. It would also become very hot.

I guess my question is - Did you buy it from a dealer or privately ? Take a quick picture of the plastic part you found and we can advise.