When connecting any controller to my girlfriends Xbox, the control will sync with Xbox and...

My sync button turns off my Xbox one X and won't connect any controllers.

When controllers do connect they disconnect and flash.

Had this problem since beginning of February.

Hi,Kash! I'm Luis, a fellow Xbox Gamer . Thanks for reaching us out here.

Since the console is already old and has never been cleaned it is more than likely for this to be a hardware malfunction.

Let´s first try a basic power cycle

1. Turn off your console by holding the Xbox button on the front of the console for approximately 10 seconds. The console will turn off.

2 Unplug the console

3. Wait for 5 minutes,then plug and turn your console back on by pressing the Xbox button on the console or the Xbox button on your controller.

If that does not work try factory resetting the console:

Press the Xbox button  to open the guide.

Select Profile & system > Settings > System > Console info.

Select Reset console.

You can also try and do a general cleaning

Use a soft lint-free cloth (microfiber cloths work great) dampened with a little bit of mild soap and water, or premoistened disinfectant wipes.

Important Power off and disconnect your Xbox console from the wall before cleaning it. Don't apply liquids directly to your console or controllers.

When connecting a controller to the xbox or pc, you can press the wireless button on the controller to sync the controller to the console or PC that you are trying to connect it to.

Is the controller new? has it been working before?

Try to press the sync button on the controller and the Xbox console. More details can be found here on connecting your wireless controller to Xbox consoles:

https://beta.support.xbox.com/help/hardware-network/controller/connect-a-wireless-controller

I bought it used froma friend he had it working on his console but when I got it the sync button was pushed in all the way. Then I opened up the contoller to find the sync button has completely broken off and rattles around in my contoller so pressing the
sync button on my controller is not possible

Read this carefully. The controller will NOT connect and there is no picture while it is on. When I Try to sync the controller to the xbox, it acts as if it found it but still does not connect.