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First Answer is obviously a scam. This is usally caused by a low battery, a low battery can be caused by an old battery, many short trips (less than a couple miles), or a bad alternator. If you just replaced the battery and you drive more than a few miles every day, your most likely fault is a bad alternator. Poor cable connections and excessive electrical resistance can also cause this, but are less likely.
The cog wheel is jammed on the shaft ,you will need to go under the can and spray the cog wheel with easing oil so it can slid on the shaft . it is just below the fly wheel on the starter motor .
dunno if the starter is bad but it has to be removed to find out. what you can try is if its a standard, rock the car in gear, or an auto, slightly rotate the engine. if that works, you may have a combo of a bad starter and bad flywheel/flexplate. inspect the teeth for major damage when the starter is off.