I've had the exact same problem as OP. I was browsing in Chrome when the backlight started flickering. Wearing headphones but with no sound, I was able to hear faint static that correlated with the darkness of the screen (when the screen was dim mid-flicker, noise was produced). I had it set to a specific brightness setting, so I switched to automatic using the drop-down settings menu. The problem persisted. I did not exit Chrome. I tapped the power button which gave a normal enough looking fade out. After about 5 seconds I tapped the power button again to power the device on. The Chrome screen I had been looking at when I powered the screen off flashed briefly on my screen accompanied by a bit of static and a slight pop, and the device went black. I have not gotten a response from the device since except for, like OP, when the device is plugged into the wall. Then I only get a battery icon with a lightning bolt for 1 second every time I push the power button.
After calling the warranty information number, Google is sending me a replacement device. They do not make you pay $400 (in my case, as I had the 16Gb) but authorize a payment of that amount so that if you do not return the device within 21 days they are not left high and dry. Seems reasonable to me.
Anyway, just adding my experience with this issue to the forum. OP is not the only one to get this symptom!