The ignition switch provides two sources of power to start the engine.
While cranking the coil gets its power from IGN 2 after the engine starts it gets its power from IGN 1.
If the ignition switch is not functioning correctly it will crank but not provide power to the coil.
To test this disconnect the yellow wire from the starter relay (That way the engine will not crank).
Check for voltage at the coil positive with the key in off it should read 0v, turn the key to run and it should read 6-10v, turn the key to start it should read 12v ( or whatever battery voltage is)
Then report back.
And welcome to the site!