My wireless controller won't turn on without being plugged in?

if you bought a secondhand you should return it to wherever you bought it from, I highly recommend not purchasing used controllers

I have 2 controllers. One that is wired, and I have separate controller that is wireless. When I plug in my wireless controller it doesn't turn on, and it makes my other wired controller which is plugged in turn off. The wired one works fine by itself. but
once the wireless one is plugged in it doesnt work. What could be the problem?

Any USB cable works in my controller (with or without battery or AA)for the headset works normally. Simply plug in the USB port of the console and controller. I believe it is some kind of wired mode. Where he turns off the wireless and works normally.

I use my wireless controller for Single player games all the time all I did was plug in the wireless receiver and it worked just like when I had a wired controller and i just plugged it in. Don't use a Controller without Auto Aim you'll get murder on the
PC because controllers are just about useless without it.

Okay. Here's a list of what I did to try and trouble-shoot the issue.

1 - Turned off and unplugged XBOX 360. Plugged in 3 Microsoft brand wired controllers into USB ports on the back. Plugged in XBOX 360 and powered on. All 3 controllers show Player 1. Unplugged each controller individually at the in-line release/breakaway
connector and reconnected. No change. Each still shows Player 1.

2 - Turned off and unplugged XBOX 360. Plugged in 1 Microsoft brand wireless controller into USB port on front (I know it's a wireless controller but this one is used and the rechargeable battery is completely dead and won't hold a charge.). Plugged in
3 Microsoft brand wired controllers into USB ports on the back. Plugged in XBOX 360 and powered on. All 3 regular wired controllers show Player 1. Wireless controller that's plugged into a USB port shows as Player 2.

Thanks.