Can't unplug play&charge cable from Xbox 360 controller

Hi there! This is Ronnie, an independent advisor.

Nice to meet you and I hope you are having a great day!

I understand you need help with your controller problem.

Actually, there is no special button that you need to press in order for you to remove the cable. The cable can just be removed easily by pulling it out from the controller. You might need to do it harder as it might just be stuck because of how tight it is. Just make sure not to pull using the wire but instead pull it from the base just on top of the controller.

In addition to the instructions from XBF Chris J, make sure that you really have a wired Xbox 360 controller, and not a wireless Xbox 360 controller that you connect with a Play & Charge kit cable.

A real Xbox 360 controller that works with PC has a fixed, non-removable cable. If you can unplug the cable from the front of the controller, that cable ONLY transmits power to charge the controller.

No controller data can be transmitted via that charging cable, and therefore the PC can not detect it. But when the controller detects power coming through that cable, it vibrates shortly. Maybe it's that why the controller "only" vibrates, but is not detected
by the PC.

As above, take the battery pack out of you're not going to use the Xbox for a while,.

There is also no need to unplug the play and charge cable (unless its in the way) If you were to leave it plugged in the console would continue to trickle charge the controller when you power the console off. If you unplug the play n charge cable because
for example it prevents a cabinet door from closing, then it may be worth looking at plugging the play and charge cable into a rear USB (unless used for wireless)

I have checked the Device Manager and saw "Xbox 360 Wireless Controller via Play & Charge Kit"..

This is why. The wireless 360 controller is always wireless, it can't be turned into a wired controller. The cable can only charge the battery, it doesn't send data.

To use your wireless controller you need an Xbox 360 gaming receiver.

Are you sure the Xbox 360 is a wired Xbox 360 controller, and not connected by a separate cable like the play and charge cable? If it is the play and charge cable, it will not work on Windows 10, as it only charges the batteries on a PC. If it is a actual
wired controller, then Windows 10 should detect and then download the drivers if needed.

More info on connecting a 360 controller to a PC can be found here
https://beta.support.xbox.com/help/xbox-360/xbox-on-windows/accessories/xbox-controller-for-windows-setup