Wired 360 controller is causing constant beeping and seems to shut down other usb devices

You say your wired controller wouldn't work either, I'm guessing it's your USB ports. These do have over-current protection and sometimes can shut down because of it. Shut down your console and disconnect everything except the power supply. Turn it on
for a few minutes and then shut it down, reconnect your controllers and see if it has fixed it.

Second, How old are the rechargeable batteries? They don't last forever.

support.xbox.com/.../controllers-remotes

This can happen to any wired controller over time.

With the constant bending of the cable where it enters the controller housing, the insulation on the numerous wires can split exposing the copper wire within.

These can then touch each other and cause an electrical short circuit.

Once this happens a new controller is required.

Hi,

Sorry bit there is no 'correct 360 controller cable'.

A 360 wireless controller remains wireless even when plugged in, it does not become wired if you connect via USB. The reason is because the controller isn't designed to send data down a USB cable.

Only the Xbox One controller works wired and wireless.

Same here. Ive also tried using the device wired through the micro usb port this did not help. The device is clearly connected as i can access the menu to shut off the console and controller and it is not a charge issue as the vibration works when holding
the home button and the issue persists with the controller wired vs wireless.

It also seems that the controller stays connected only when I'm holding the USB wire at a certain angle (pressing down on it). Once I let go of the wire, it disconnects.