So it sounds like either camera is bad or the power supply has gone bad. Do you have another camera / power supply you can try swapping just to test it?
If it is under 1 year old then Google will most likely honer their 1 year warranty and replace either part. It is longer than a year you are out of luck.
Here is the link to open a support ticket if you want to which will get help directly from Google...
https://support.google.com/googlenest/gethelp
