Definitely do the faulty/returns procedure. If you try to fix the ring it's not going to be eligible as a return item because it'll seem like you caused the damage.
For what it's worth, I used my classic ring like that for an age before giving it to a friend to test devices. The failed inlay is workable when it's pressed the right way, it's just scary to do that on a phone.
The alpha I've tried a couple of repair techniques with varying success. I first lost my public inlay, regained that function for a fortnight then lost it again. At the moment I've got it back but the private inlay is dead. (This is due to my interference, attempting to reflow the broken solder joints. It's not recommended or advised and it does completely invalidate any warranty.)