welcome to the joys of magnetics and electricity.
if theres no reading between blue and white, the coil is internally open circuit. dead. almost impossible to fix unless your patient and want to make a coil winder. theres 2500 turns of .05mm wire last time i checked...
after all the time and effort...just buy a new coil.
the coil between the blue and white wires delivers the main voltage to charge the capacitor, and should read, even with a lousy multi meter that is NOT intended for this use, somewhere in the 60-70 type volt range...
if you get a reading of only a few ohms between white and black, thats normal. and that coil rarely burns out as its heavy guage wire.
and the voltage between blue and black should be around 6 volts.
yes, the two coils are in series with each other. black (earth) to white, in heavy guage, then white to blue, in light guage.
the reason you DO get a reading when turning the engine over, is because the coils are still there. theyre still conductors, cutting lines of magnetic force. just because one end is waving in the breeze doesnt matter. theres a voltage produced in the conductor. being AC, electrons surge that way! then back again! and the conductor, having some resistance, allows a tiny lil current to flow, despite there being no complete circuit!
(Tesla, the leading man of AC, made many devices that operated with only one wire, and no apparent "return circuit"s. dc is hard enough. once you deal with hi frequency AC things get weird!)
while you might read 2v or so, the current available is sweet f all... if you tried inserting a 10ohm resistor, added some load to the circuit...well, you still would only read 2v or so as the circuit isnt a full circle due to that open circuit inside.
like a mains transformer... say its rated at 12va. thats 12 volts at one amp. if you increase the load, (less resistance) the voltage drops. the current increases proportianally to the change in resistance or load. if you remove the load, infinite resistance, the voltage "theoretically" is infinite too. youll find an unloaded transformer of 12v may produce 15 or 20v across the secondary.
in this case, the multimeter has its own resistance of a few megohms, which still allows some current to pass, that due to ohms law... lowers the voltage being read. your measuring device affects the measurement. thats why the impedance of a voltage tester is so high. less current flowing, less effect on the voltage. current is the reverse. you want as much current to flow through the meter as possible, so it has an extremely LOW impedance.why you NEVER attach an ammeter across the outputs but wire it in SERIES with the "load". an ammeter is basically a short circuit.
you would more than likely get the same reading if you just disconnected one lead on the multimeter...
on the cdi unit itself... you shouldnt get anything between blue and black wires. the diodes are reverse biased and wont allow any current to flow. (edit...in one direction. i forgot about the trigger current flowing the other way... )
if you had one of these aftermarket cdi's where you can access the wire that feeds the ignition coil... between that wire, and the blue wire, with the multimeter set to ohms...in one direction, you would get a constantly increasing resistance, as the main cap charges. reverse leads, and you would get nothing, as the diode prevents the cap from discharging.
if you measure the resistance of a capacitor...it will increase, until cap is charged fully, then by reversing the wires, you get NEGATIVE resistance as the cap discharges!. same deal with certain types of mosfets
basically? just get a new magneto