Nexus 7 won't boot up - could it be due to cell phone sitting on top of it?
It could very well be due to your mobile sitting on top of it.

There may have been an electrostatic discharge from your phone, that was sent through the Nexus 7, breaking/harming some components.

If you can, I would suggest you take it to the repair center - it would be the only way if this is what has happened.