Hmm, I'd try a cheap analog meter (with the little needle, not digital) across the pickup coil (left side of engine, under the round cover with 4 screws), check the resistance first (ohms), you should get some continuity reading, (unplugged if course) then spin it up (starter), the needle on the meter should flicker to show you're getting signal. I've seen many vehicles (especially bikes) where this pickup coil failed causing these exact symptoms, sometimes the wires chafed or cracked and grounds the signal out too.
good luck