Are you using starter fluid? I would not try to wake an unwoken engine without it.
Engine was rebuilt about 4 years ago and I got it started last year without starter fluid. Fuel is making it to the carburetor float bowl and it is wanting to start. But maybe I need to buy a can.
Charge up the battery. 12.4 volts on a 12V battery is mostly discharged. You're starter is probably dropping the voltage available to the coil while cranking to the point where it can't fire the plugs.
Just put the trickle charger on the battery. 🙂