The starter could very well be the problem. You should have a mechanic to check the wires leading to the starter first to make sure they are not loose. It could also be the alternator or battery having a charging isue as well. Have a mechanic check the charging system as well.
Try to replace the starter relay
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solenoid needs replaced but instead just replace the whole starter
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no do not recommend tranny will start slipping just drain and fill or drop pan and replace filter and gasket
remove it from the engine
replace coil
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