iPhone is dead, will not charge
There are a few possible things that could have happened. I've ordered them (and their solutions) below from most to least likely.

Explanations:


You have a faulty cord.


It has become frayed on the inside.
One of the metallic connectors is dirty.

Dust or dirt has collected in your charging port.
Your wall outlet is not functioning correctly.
You have a hardware problem.


Your charging port has become disconnected internally.
Your battery is defective.



Many of these cause your device not to charge. Thus, powering on your device does nothing.

Solutions:


Get a new cord.


Manually repair the wire by soldering the frayed ends together and using a heat-shrink to put everything back together. (You probably just want to buy a new cord.)
Clean the dirty connectors.

Clean out your charging port with a folded index card, toothpick, plastic card, etc.
Call an electrician.
Take your device in to get fixed. (Hopefully, you have a warranty.)