1993 Jeep Cherokee Bypass Altenator

Hello, I don't believe your alternator has anything to do with it? Make sure the battery has a full charge and the cables are ok. Then, I would check the circuits at the starter relay, in the power distribution center under the hood. The voltage for the switch side of relay is usually hot all the time. Voltage for the control side of relay should go hot with the key in the crank position. With an automatic, you might try cranking in neutral.