4/ Is your battery accessible? (I think for the Acer E3 it is)
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5/ Can you visually inspect it to see if it is swollen? (I think you can inspect it)
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5/ Can you visually inspect it to see if it is swollen? (I think you can inspect it) => swollen = bad, may not hold charge, replace it.
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6/ Will your phone turn on and work if connected to the charger with the battery removed?
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6/ Will your phone turn on and work if connected to the charger with the battery removed? => replace battery and try again to see if new battery will hold a charge.
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If you rule out all of the above, let us know to investigate further, as it could be the charging dock (where the charging cable plugs into the phone), or something wrong on the logic board, etc.
1/ Not the charger?
Ok,
2/ Not the cable?
3/ The wall plug/adapter if any?
4/ Is your battery accessible?
5/ Can you visually inspect it to see if it is swollen?
6/ Will your phone turn on and work if connected to the charger with the battery removed?