Can't access FastBoot mode & sporadically won't power back on after I attempt it!

When it's working, my brand new Nexus 7 2013 Wi-Fi powers on and off normally when pressing and holding the power button for 3 seconds. But when I attempt to enter FastBoot mode (I plan on rooting it) by pressing the power & vol up/down simultaneously, nothing happens, just a black screen as if the device is dead. What's worse is that I then have great difficulty getting the Nexus to even power on normally. Right now it appears to be dead but if I press & hold the power button in many attempts it might come back on. This always happens right after I attempt to enter fast boot mode. Using Android 5.01. Can anyone help me with this problem? I'm on the verge of RMAing it since I can't seem to get it to power on anymore but will keep trying. I really would like to root this but it seems impossible at this point.