How do I find wiring problem on Murray riding Mmower?

Murray 40 inch cut, bought in 1984 was running. Now will not run at all. New battery, new spark plug installed. I have jumped out safety switches trying to see if that's the problem. Mower will not run with them hooked up or jumped out. It was running. I switched it off, won't do nothing now. I checked solenoid with 12 volts, it's working.Coil appears to work as I applied 12 volts to it and magnet field started. Key switch continuity checked good on ground. With power going to lights when turned to start then back to lights power there. What am I missing? Could alternator be bad and cause nothing to happen when you turn key to start? Seat switch been gone for years.