For the Purpose of Detect Magic and Identify. Would a Magic item that ran out of power for the moment be considered a magic item?

If a magic item runs on "Magic Batteries" when the Item is out of power would it be considered a magic time for the purpose of the Identify and Detect Magic spell?

For example, I have a Mirror that shows through illusions, it has crystals around it that are destroyed as you used it, you can replace the crystals for more uses when it has no crystals, would it still be considered a magic item detectable by the spells?

Would the same work for items with charges that recharge at dawn? If the item has 0 charges and is not dawn yet, would it be still be considered a magic item?