Tim, my first reaction is this may be the bayonet, and its inherent unreliability.  But, it does seem strange that all 4 globes are not working.  With the game on, do any of the globes light whilst moving the globe around a bit with your fingers?  Another check would simply be to see if you have voltage across the leads.

I have found time after time after time I am always "fixing" light bayonets (at least the vintage used in the 1970s, especially ones on Ballys).  This is along the lines of Clay's guides.