okay, so you've removed the battery as a possibility in the equation...
that really only leaves the starter motor, if you leave your bike cranking over for 5 minutes then it is likely to cook your starter motor and drain your battery, anything more than 5-10 seconds on the starter should be plenty to start a week two-stroke, if it isnt starting on the peds battery but is starting if jumped from a car it could likely be that the starter is drawing too much current for the ped battery and not leaving enough power to spark to crank over, had this problem with my XJ600 once when it had a dodgey battery on it, used to bump-start it everywhere until i got a new battery but seeing as yours is variator driven you wont be able to do this,
make sure your battery is fully charged and put a voltmeter across the terminals before hitting the start button, within the first few seconds note the voltages, anything much below 9-10 suggests too high a current draw for the battery (knackered starter or shorting solenoid), not so much a problem on 12v batteries but that sort of problem on a 28v aircraft battery has enough energy to weld... keep that in mind when playing with wires