I am not an electrican but a physics/electronics teacher. As you described .... to get the tester screwdriver to work you can have an electrical path via your body to the floor to make the neon light .... this route will carry the small current needed ... you do not need a working neutral wire to make this happen.
It sounds to me that the pin connections for the lamp to fit into place are at fault. It could be that either or both of them are stuck down. In attempting to repair switch off the mains electricity.
Remember - just because the lamp doesn't work it doesn't mean you can't be given an electric shock.
best wishes Nyge, March 2011