Is it EFI? Which means it probably has an ECM/ECU to go along with it. To kill the engine, it's usually a matter of grounding out a CDI wire, but the ECM or other relays are in the circuit as well (to protect it from theft). I've heard the key switches lose their ability to make contact when the key is turned (the internal electrical contacts wear out or get overly corroded), it's an option to try. Otherwise, make sure the key switch has a good ground to it. Get a manual and wiring diagrams and see where you can follow the problem. You'll need a multimeter. I've seen the EFI's have diagnostic plug-ins available that could reveal codes within the ECM/ECU.
Does it shut off with the kill switch?