FWIW, stator failure is common on the old KDXs. You still can get a spark, but just not strong enough.
It's hard to diagnose, and the problem can be intermittant at first (first, the bike gets hard to start cold, then it will cut out when hot and not restart until it cools down, then eventually it just will not start or run at all). Since you are a new owner, you don't know if the problem came about gradually over time.
You may want to replace or rewind the stator. There are some measurements you can take with an ohmeter, but when mine failed, it still measured within spec.
You will have to remove the flywheel to get to the stator.