Your Ringly should pulse red every few seconds when it's actively charging. If it's fully charged, it will flash green once. If you're not sure, you can take it out of the box and drop it back in.
Under your ring, there are two charge pins that need to make contact with the pins on the box in order to charge the ring. Make sure the charge pins are making contact when you drop it in the box.
Please try cleaning the pins with a little bit of rubbing alcohol - if you have it - and a soft cloth or q-tip, in case anything such as sweat or hand lotion got on them.
If it still doesn't light up, please try using a different micro USB cable - if you have one at home - as well as a different power outlet.