I'm sorry to hear that you're not having any luck with the ring! Support queries are mostly sent to the forum first to make sure that it's not an expectation/usage issue first and also to make sure that people understand their options when they have an issue like this. The ring exchange and return procedure is pretty well laid out (and wonderfully simple) but it's best if you're 100% sure that it's necessary first. Also, your actual ring order should automatically come at a later date when the manufacturing issues have been fixed up!
Let's get a couple of things out of the way first up, each ring that gets sent out is fully tested and working when it leaves the distribution center - it's possible that an inlay can go bad due to postal workers playing football with parcels but it's not common so for the moment lets assume your ring was tested and working, and is quite probably still working.
The tags, any NFC tags really, are a different proposition to the rings themselves, it's an established fact that metal will interfere with NFC devices and change the way they function. This issue has been partially sidestepped by the NFC Ring team when they designed a special 'absorber' layer to go between the inlay and the ring body, and when they tuned the antennas in the new custom built inlays. This leaves the rings most definitely working on a fully functional NFC system in a phone or other device but can leave you out in the cold if there is anything "off" about your NFC reader at all.
To make it perfectly clear for anyone who reads this, a poorly functioning NFC reader will often actually work "properly" with a standard non metal NFC tag. Using a Classic ring on such a device however can sometimes leave the ring bearer in a world of confusion because other tags work so it must be the ring... when more often it's the device you're trying to use the ring with.
This issue can sometimes be cured by changing the ring from a Classic to an Alpha, which has a larger antenna and is therefore easier to read with devices which aren't 100% working. But remember that using a ring that is easier to read does not fix your NFC device, it's just shouting louder at a half deaf person.
My advice would be to test the ring you have on as many other devices as you can, I'd bet that it will work on most of them, if not all. Do this just to assure yourself that the ring works. Also contact email@example.com and ask them if it's possible to change to Alpha, refer them to this thread so that they have any information they may need. Assuming an Alpha does the trick you would need to do this for your proper order at a later date as well, so best to let them know about the issue now rather than end up with another Classic ring which your device doesn't like.
If you'd like to chat about any of this then private message me and I'll give you my skype address. I'm easy to chat to and can help address any confusion or concerns you have.