As I remember, nothing showed up, though I wasn't really looking. Nothing on screen, and since the device was technically off, nothing on the computer screen either. If the device does have some battery left but is actually frozen, you should be able to force-restart it by holding the power button for around 10 seconds. If even that doesn't work. Pull the battery. Yes, I know that Nexus 7 has a sealed battery, but the back cover can actually come off pretty easy. Though, that might void your warranty, not sure. I already had the bootloader unlocked on mine when I opened it up, so I didn't have any warranty to begin with.
Just use a knife (should definitely use a dull knife, or even a butter knife) and carefully pop off a portion of the back cover. Don't use too much force, just enough to slide a blade in between the back cover and the main body. Then just use your fingers to pop off the rest. The battery is held in place with glue, but the cable that connects to the motherboard can be unplugged without removing anything else. So unplug that, and reconnect it. Let it charge for a while on an actual charger, not PC connection. If afterwards your Nexus 7 doesn't turn on, whether it's the OS, Fastboot, or Recovery, then I'd say you're proper fucked.
So, your options seem to be:
try to sort it out through software - though since it completely unresponsive, I'm not sure that'll work.
get a replacement through warranty - pain in the ass, you have to wait, and you probably have to pay for it in some way
try the method I described - which might void the warranty, rendering option 2 useless.
and worst case scenario, sell it for parts - which is what I did when I accidentally cracked the screen on mine.