I had the same problem two days after I bought mine. I took awhile, but it eventually came up. All was well for a couple of days, and then it happened again. I checked this out on the internet, and one guy said that, if you hold the power button on for up to 30 seconds, it will come on. He was correct. The 30-second routine became the norm for awhile, and then all was well.
I called the tech folks at Google. They described this as a problem. Had I bought it from them, they would have replaced it. I checked with Gamestop (where I bought mine) and had no problem replacing it. I am a newby to this forum and pads, but I have been an electronics tech for over 35 years, and was concerned that, one day, the thing wouldn't come up at all and be out of warranty. My advice to anyone having this issue is to replace it.
By the way, mone was a 16GB with a serial number that started with C80KBC. So does the replacement, so I have my fingers crossed!