This is going to be sound silly but you are holding down the power button for a few seconds to get it to turn back on, right?
When a phone's battery is completely drained it may take a longer time than you're used to for it to gain enough juice to power on again - sometimes up to 10 minutes. I would say just wait a little while longer before trying to turn it back on. Also make sure you're plugging it into a wall adapter and not a computer's USB port - the former puts out higher amperage and voltage, which will charge your phone properly. Plugging it into a computer is more commonly used for transferring data and will consequently charge much more slowly.