Idling good start good but stalls if pressing throtle

Check the charge on the battery, should be at least 12.6 Volts DC, then look for loose or corroded connections, starting with the battery cables.

sounds like the switch may be shorted, or a wire(s) have shorted to one another.... Find the plastic connector for the switch and unplug it... it should not fire.. if it does.. maybe someone has hot wired it??? ... BE CAREFUL!!
2005 Arctic Cat 250 300 400 500 650 ATVs Service Repair Workshop Manu
Arctic Cat ATV repair manuals
Arctic Cat ATV Service Repair Manuals
Arctic Cat ATV Service Manuals Online

Pull the carb and have it cleaned and rebuilt.

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sounds like it has been sitting, if you have never rebuilt a carb, best to bring it in,, the main jet is probably all gummed up,, you can try draining all your tank gas,, spraying carb cleaner into the carb after removing air cleaner but that really wont help out the main jet.. Stabil is a good product for gas if you are going to store your ride for awhile, it also acts to clean carbs while using a small amount when you fill up.

On the amp meter there are some slip on connectors. Check there.

This model uses an electric choke, it may be stuck on.

vaccum leak ? hoses cracked at connector. intake manifold leaking ,cracked ?

Clean carbuator

is it running out of gas? backfire is caused by a lean condition. I'd check the fuel path from the tank to the carb and clean the carbs. could have something floating around in there occasionally blocking fuel flow.