What year/model is this LC4? If it's 2003 or newer then the stator has no effect on spark (until the battery runs down). The CDI gets it's power from the battery through a bunch of switches. On the '02 and earlier bikes the orange wire at the CDI has the power. If your bike's newer, check the wiring diagram to figure out which one it is. Look for 12v there. If it's not getting power then check your wiring- including the safety switches.
If the CDI is getting power, listen for the flyback. With power going to the CDI it should create a very faint whining sound like a tube TV. I don't know if that is a good test, but it's easy to do. Also check the pulse generator. With an AC voltmeter you should get something (between a fraction of a volt and a couple of volts) from the pulser coil when the bike is cranking.
Checking the coil with the battery is a good idea. However, I'd suggest that in the future you use some sort of ballast- like a 10 ohm resistor or a turn signal sized light bulb. The coils for a CDI ignition aren't designed to take continuous current from a battery the way points ignition coils are and they can burn out quickly.