Chosen Solution
Not sure if this one is a 1708 (label in battery compartment has been removed). It’s definitely red! I’m not the first owner, so I don’t know the history of the controller. The Sync button would blink once and go dead when pressed. The controller works as expected when a micro-USB cable is connected. After disconnecting the micro-USB cable and attempting wireless connectivity with known working batteries, I noticed the controller works as expected when the Sync button is HELD DOWN. I then hit the B button and the console asked which controller am I using (as I had a working 1537 already connected). Releasing the Sync button turns off the 1708. The only other defect - the Pause/Menu button (just left of the X button) fails to engage at all. All other buttons and joysticks work as expected and tested with the Game Controller Tester app for Windows 10. What should I examine when I take the 1708 apart in addition to the silicon front button assembly? Where can I get replacement microswitches for the Pause/Menu and Sync buttons? This question might be cross-posted elsewhere.
This still feels like power issue to me. Try with BRAND NEW batteries, or use a USB power bank/phone charger to power the controller, but not using USB to connect to the PC. If it works with external power, then either battery does not have enough voltage or something is wrong with the power circuit.