Any easier way to fix this broken ground wire in bathroom?

An apartment i manage has a light fixture over the medicine cabinet in the bathroom. The lights flickered on and off for awhile and then went off and will not turn back on. I have rewired everything to ensure good connections, but the lights still dont work. Basically have narrowed it down to a broken common wire, have power at the light socket when i ground the tester to the copper ground wire, but not when grounded through the neutral wire. Also the outlet on the same wall quit working at the same time. Is there an easier way to fix this without trying to run a new wire all the way through the ceiling?