Looks like the dome is the same as Chexx??? Measure the width and length where to dome attaches to the base and also measure the space between the holes where the screws attach the dome to the base! Be interesting to see if they're the same as the Chexx ones! If they're take it to your buddy and see what he can do. If he messes it up more you can either buy a new one or go with a used one that is in better condition than what you got!
As for the broken player, again if it's like Chexx, you should be able to take all the guys off buy just pulling straight up on them! Take them all out and then the one that is broken you can take the gear box off the end of the rod. This should allow you to turn the gear box and, hopefully, allow you to use something to punch the broken peg out!
Be interesting to see pics of the gear boxes to see if they're the same as well!!!
I see the base is all wood!!!! Unlike Chexx is plastic!