My Xbox Series X controller won't turn on?

I don't have an Xbox Series X, but I bought a controller to play on the PC. When I try to turn on my controller, the Xbox icon lights up, but when I let go of it, it turns off and doesn't work. It only works when I connect it with a cable, but I want to play wirelessly. Can someone help me?

Otherwise change the batteries, if that doesn't work, connect a cable to the xbox. If that doesn't work either, screw it open carefully and see if a cable is loose or torn off. If one is on then plug it in and otherwise solder. It's best to watch a video on how to open the controller before something breaks