Samsung Galaxy S4 - Should I replace the power button or usb port?

I forgot my phone in the car overnight on low power, and it drained to zero. When I recovered it and try to turn it on, nothing happens.

Sometimes the phone will vibrate when putting the battery back in or plugging it to a micro-usb cable. Sometimes the phone will vibrate in these instances and flash a moment of the booting sequence on-screen. Sometimes, also, the vibrating will become repetitious and the phone will vibrate (as if it recognizes it's charging) ever 5-or-so seconds for a little bit, while never displaying the charging symbol or the red light.

One thing to note is that the phone doesn't heat up while charging or whenever I press power. It does feel as though the phone is off, whether the screen is black or not.

The symptoms seem similar to this video that links this to a power button problem:

However, the cold battery repetitious vibrating makes me think that there is some issue happening in the usb instead, or as-well.

What do you guys think? Thanks in advance!

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