Try removing any covers that you can without breaking anything, then fill a container with uncooked rice and push the player into the rice and cover the container. Leave it like this for a week or so.
Either the left headphone is shot or the headphone jack is messed up. Try a different set of head phones if its same result see about replacing the jack.
The battery does not hold charge. It is weak. Replace it with same type number. Brand name of the battery isn't a matter, check its type number printed on it.
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