92 cutlass supreme starting problems please help

my mom has a 92 olds cutlass supremem 6 cyl. Her car will not start, it is just clicking under the hood on the drivers side by the engine somewhere, not the starter. I took the starter off and had it checked, it was fine. I put it back on and the car started perfectly. I turned it off and tried to restart and it would not turn over at all. I thought that maybe the starter was going bad so I bought a new one just to test it with. I hooked it up and it also did not turn over. I put a test light up to the wiring on the starter and the test light came on when the key was turned. I dont think that the car has a starter relay? I dont know what else to check, please help.