Answer to "Why is my controller not turning on?!"The port on the controller has the bad connection. Try cleaning off the contacts. If that doesn't work, check out the micro USB connector repair guide.
Answer to "How to replace or fix a damaged USB plug"Follow the teardown instructions for the Afterglow Prismatic controller. Using a voltmeter, check continuity from the gold contacts to the right of the USB connector. In the view in the image below, the order from left to right is: Pin 1 = V or VCC Red wire Pin 2 = D- or DATA -1 White wire Pin 3 = D+ or DATA +1 Green wire Pin 4 = G or GND1 Black wire Pin 5 = Shield1 (also ground) Check each gold contact with it's corresponding pin on the front of the connector as well as the remaining 4 pins to make sure that contact isn't crossed or shorted with another pin in the connector. The G and Shield1 should be the only 2 that have continuity with each other. This is why there isn't a gold contact on the board for the Shield1 pin #5. I suspect that the solder or trace on the board for Pin 1 is either getting broken or shorted to metal on the connector, since the trace runs underneath the connector and wiggling the plug would cause the controller to intermittently turn on. If it looks like the solder on the...
Answer to "Why won't it turn on?"The USB connector on the controller is damaged. If you have the tools and ability to do so, unsolder the connector and solder on a new one. Update (03/24/2019): Afterglow Prismatic Wired Controller for Xbox One Micro USB connector Replacement