Try using a different micro USB charging cable. The power button and ABXY buttons should flash when first plugged in. Then later it will just be the power button flashing until full charge is reached. The power button will then glow solid blue.
If you cannot get it to start charging and can return for an exchange or refund do it. If you can’t, you can try fixing it yourself.
The battery is a Li-ion battery and in most cases can be brought back by forced charging. Open the back by removing the screws that hold the controller together (note the one under the quality label below the reset hole).
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Remove the cover and unplug the battery.
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Measure with a voltmeter. If it is below 3.2V the charging circuitry in the controller may not allow the battery to charge. I used a cheap USB cable and modified it so I could apply the 5V USB power via soldering needle probes to the positive and negative wires. The data wires were cut short and taped to prevent shorting. You can use something like that to charge the battery directly. Once it is above 3.2 V, you should be able to charge it normally.