1997 Pontiac Grand Am engine sputters, dies and then won't

Engine was running fine when cold. If restarted hot it will die within several miles. Then it won't start. I installed new ignition housing, plugs except for coils and ignition control unit. Still the same problem, starts cold, but won't when hot. While diagnosing the ignition control unit with voltmeter, (which seemed to pass tests) the starter got very weak and now just clicks when tried. I thought it was the battery and switched a good one from another car. Still the same clicks. I checked engine ground and cleaned, checked fluids still the same clicking noise. This problem keeps morphing and I can't seem to figure it out. What is wrong? Is it the computer in the car? Or the ignition key switch or what? Please give me some choices to try. I don't believe it is the security system. I tried leaving the key on for 10 minutes and then trying to start, same result.