A coordinate system is not required for the Go To XY tool to work.
Being in Layout view as Dan Patterson mentioned, will limit the functionality (no graphic elements seem te get added, but flash works).
In case you don't see this interface appear in ArcMap, I might be because you have worked earlier with two displays and it may be showing on the other (not connected) display. If this is not the case, you might need to remove the Normal.mxt or consider installing ArcGIS again...