Lost key to 1998 Polaris 400cc 4x4 need to start it.

If you ran the quad with a dead or no battery, all the light bulbs could have blown from high voltage.

you can buy new key and ignition switch sets cheap on amazon

You have lost your charging circuit. Check the Stator. You can go to YouTube and watch how to do this.

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Sounds like the jets are cloged up you will need to pull off the bole and clean the pre jet and you shuld be fine

sounds like a safety feature or possible a loose conection to a wire somewhere and when its jarred from a bick bump or hill it engages

sounds like lack of compression

Carb is gummed up

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Sounds like two diffrent problems ,but the leaking of the coolent could be radiator ,bad hose or thermostat .If the oil is leaking it might have a sensor so you dont blow the motor ..I hope this helps ..If any thing please call local Polaris dealer so no futher damage ..Have a great xmas !