Dumbfounded. 340 will not start.

My first suspect would be POOR SUPPLY VOLTAGE. Even if wired correctly, problems in the bulkhead connector, ignition switch connector or switch itself could be a problem.

1---CHECK whatever needs to be grounded. If the "box" is the ground, clean it, use a jumper ground wire, use star washers

2---CHECK the supply voltage CRITICALLY. With engine off, but key in run, supply voltage should be "same as battery." Not 1/2 volt below, or one volt low, but SAME AS within a couple or three tenths of a volt

3--To be sure, BYPASS or disconnect factory wiring, use a large such as no14 clip lead, and "hot wire" the ignition direct to battery

4--Coils can go bad AT ANY TIME even new out of the box. Swap a known good coil

5--Coil WIRES can go bad, as well as carbon tracked/ cracked or otherwise conductive rotors and caps. I once "knew" a rotor that at first glance looked fine. It had a "bad?" spot right under the rotor button that was carbonized and would conduct almost all the spark straight from the button to the top of the dist. shaft!!!!