Clicking noise is usually from the starter solenoid. Try jumping the starter solenoid (jump the 2 largest leads going to the solenoid.......may both be red) and see if it starts. If it does, you need a new solenoid. If it still does not start after jumping the solenoid, you may have a bad starter or bad bendix in the starter.
Battery going bad might indicate a bad rectifier/regulator, but should't effect starting unless battery voltage is too low. Battery that goes bad in just 2 weeks was bad to start with, or you have a voltage drain someplace. 12.6 v is a little low for a fully charged battery. Some of these 2 strokes need all the voltage they can get. Try pulling your car battery and see if it will start on that.......could indicate a bad battery.