Less than a year old. I tried three different chargers plus also tried charging via USB port on computer. Also tried holding off button for 20 seconds. None of it worked. Finally today I got around to calling Amazon. Apparently they had a software code issue some time ago and my Kindle was one of the ones affected.
A new Kindle is on its way although I'm a bit 
as to why they didn't email me to tell me there was a problem with my Kindle (I assumed it wasn't charging due to something I was or wasn't doing). Having said that I'm impressed at how quick they were to arrange to send out a new one.