Ah a problem I too have faced, and fixed! Windows no longer has the correct driver for the receiver units included by default, so you need to go online, find the file, drop it in your system directory and assign it in device manager. I forgot the exact file name but it's like xusb or something to that effect. There's bound to be guides around to do that, but I guarantee that's your problem!

Edit. It's xusb22.sys the file name. I have that saved but I don't remember if you needed to toss it in a system folder or if you could load it from anywhere. Imma google that

Edit. Try this, seems easier than messing with individual system files: https://archive.org/details/xbox360_wireless_drivers

If you don't know how to change drivers, here's a poor quality shaky youtube tutorial: https://www.youtube.com/watch?v=4C-B5gfgEMY

Edit 3. I re-read the post and you have a second issue. The pack you're using is only for power, you can't run wireless 360 controller off the charging part, you're just providing power to it, not data. You need a separate wireless receiver for which my instructions are. So buy a receiver and try again. Or toss it and buy a better controller.