Suzuki atv only runs if you hold the starter button in

Sounds like the nuetral detect switch is bad or the wiring to it is cut. This sensor is on the transmission hub.

dead battery fuse blown poor connections

fuel system dirty someplace. carb ,filter in tank, inline filter or air filter dirty. clean or replace as needed.

Hey Brad
With the info you have provided, it seems to point to the ignition switch as the problem. (the clicking you should hear comes from the solenoid contacts - not the starter button). There is probably one wire in the switch that has broken or come unsoldered or other wise not making the right connection.

More than likely the stator coil or the igniter module is defective.

Turn over is the process that an engine makes when it is trying to start. If you twist the key and get nothing then it wont turn over. Google shimming a starter and watch the vids.

it could be the transmission neutral switch or if equipped the clutch switch

charge or replace your battery

switch ok ? yes . check 1st bad wire to starter, 2nd bad selonoid , last grounded starter ,

#! fully charged - good battery with CLEAN terminals and wire connectors. Starter is easy to rebuild.. If its not starting..try gently tapping starter with a dead blow hammer while holding the starter button down, if it turns over.. rebuild the starter...NOW. Make sue all connections are tight..