If you’re running Win7/8.1, the driver situation is hot garbage at best if you want to be generous about it. Since these accessories weren’t added after the fact in Win10, it actually works somewhat reliably. It’s a well known problem with pre-Win10 systems.
The fix to this is to go into Device Manager and remove the controller and driver to start fresh. Refer to this guide to reinstall the drivers after removing them from the system. If it happens again, you will need to do this procedure again.
Since the drivers didn’t fix the problem, I would question the USB cable you are using. If you are using a generic retail cable, most of these are poorly made and tend to fail. Get a quality cable from Anker and try that to see if it helps. If it does not, you may have an issue with the bottom motherboard. You’ll need to find a 1967 board if you choose to do the repair as there are a few differences between the boards I’ve personally noticed you can’t ignore and you HAVE to buy this used as it is a PCB and Microsoft does not sell parts. A donor may be the only economical way to get it as well. I don't recommend repairing these anyone since the 1708 has been out for a few years and fixed most of the part quality issues with the 1537/1697, but it can be done if you want to try and salvage this one.
If you are using a Play and Charge cable, these block out the 3.3V signal if you do not have a battery installed, and only allow the 5V signal to pass through without one installed. You will need a battery in the controller to use these to even have a chance since the 3.3V signal is critical and this is what they block with this cable.