Well it seems like the gamepad is working perfectly fine with no range issues, not sure why the Wiimotes won't work. I press the sync button on the Wii U and it does absolutely nothing. I also tried pairing them using the home button method and no luck.
How are you trying to sync? Are you just using the sync button or are you using the menu?
Hit the home button on the gamepad and use the touchscreen to get to the controller options. There's a 'sync' option in that menu.
So you hit that (which sets the WiiU to 'look' for a controller) and then hit the Wiimote.
If that doesn't work, you need to clear the Wiimotes from their affiliation with your Wii console. You've ruled out that they're not broken, so there's no reason to have them synced to that old console, right? Reset the Wii Remotes.
- Just to be paranoid, make sure your old Wii is unplugged.
- Remove the batteries from the Wii Remotes.
- Wait a couple of minutes.
- Replace the batteries, re-sync the Remotes to the Wii U, and see if the problem is resolved.
If the remote does not operate normally after checking all of the above, press the POWER button on the Wii U console and make sure the Power LED is red, and then unplug the Wii U AC adapter from the wall outlet. Wait two minutes, then plug the AC adapter back into the wall outlet, turn the Wii U console power on, and try using the remotes again.
Come back to me if that doesn't work.