i do understand that you did replace the battery( which was not noted before, so i assumed it was not replaced)
because you ran the atv on the battery, and your charging system is obviously not working(now i know you just replaced the battery) you have probably damaged the battery by running it down to 0 volts.
if the battery tests bad, you need to replace it. if the battery tests good, i highly you at least change it for a new one, so your battery memory is not vastly damaged like on the new one.
by running the battery down to 0 volts, it has ruined the memory and that battery will not last a year. a good new battery properly maintained will last at least a few years. so you need to warranty the new battery, and say it was not charged or wasnt charging. they will honor their warranty, then we can start with a fresh battery to do testing.
the first tests we will do is run the atv and check voltage at the battery posts with the voltmeter or (multimeter on the DC volts setting) at idle speed.(you said you checked it, but i want to start from step 1, so i know all the test results as they happen)(no offense) after you check at idle speed, rev up engine about 1/3 and read results.
i am sure your results will be at 6 or less, and will probably go down as you rev the engine, and the ignition system starts to draw voltage off the battery.
we will continue from there to test your charging system, including the stator(which produces ac voltage) to the regulator/rectifier(which changes the ac voltage to dc voltage, and then regulates what goes back to the battery for proper charging voltage).
you will most likely need to replace your stator assembly and your regulator/rectifier(this is one component) as it is probably damaged by the bad stator.
after you replace the battery, test the idle speed and 1/3 throttle speed, and read me your results.
thanks for the patience, and we will get this problem fixed.
PLEASE let me know if i need to explain something again more clearly. i sometimes catch myself going on about stuff)