Is the Run/Kill switch in the RUN position ?
Try flipping the switch several times.
There is a 10Amp fuse, after the main fuse (30 A), before the Kill/Run switch. Test/replace it.
I think the fuses are under the seat, back by the battery area.
Install a new sparkplug.
Other than those, the rest are more expensive:
CDI box, Ignition coil, ignition switch, wiring
and less likely to sudenly fail.
If there a Kymco Dealer near you ?
Do you have a service manual (I think you can download one).
Good luck.