There is no test for a CDI as far as I know.
Also never seen one fail. Never suspect the CDI...
FIRST, Change your spark plug with a new one and try again.
Then change that new one with another new one. I have had NGK spark plugs bad, out of the box.
You need to take 4-5 measurements, whether these components are new or not.
1. Resistance through the secondary coil (Ground to plug cap)
2. Resistance through the primary coil (Input terminal to ground)
3. Pickup coil resistance and continuity
4. Killswitch continuity when set to KILL, no continuity when set to RUN.
5.Verify the CDI/pickup coil/ignition coil has good grounds. (You will need a wiring diagram for finding the CDI grounds.)
Report back and we'll see where you stand.
Good luck!
-BIG DAN