The interesting thing about accutron watches is that they won't run until you replace the case back. You won't hear the typical tick tick of a standard watch but rather a humming sound comming from the tuning fork. Try putting the chase back on and screwing it down and then look at the sweep seconds hand to see if it is moving. If it isn't, listen for the humming of the watch. If you hear that then you will need to take it to a Bulova accutron trained watch maker for service. What ever you do, do not take it to a normal watch shop because it takes special training to repair one of these watches.
It is well worth spending the money to have it repaired if that is what it needs because it is a piece of your family history and should be passed down to the next generation family member along with some of the history of your grandfather. PRICELESS.
It is a lovely watch and something to be proud of.