Friend bump and hey I can't remember if I got one or two broken Sega controller from you but I just got done fixing two of them
It seems (I didn't test this) the buttons are pushed by small magnets in the controller on each pushable button so I reseated and cleaned off the (what I assume is) magnets and they seem to work. They can be a little touchy and a bit more pressure is needed to get it to register but at least they work