Many things could cause it, but the battery might be too dead to stay on for more than a few seconds. Give it 5 or 6 hours of charging while off before you try to turn it on again. Make sure it is charging. The outlet that the charger is plugged into is powered. The charger is working. (It's probably a micro-USB charger, so try charging some other device that uses micro-USB.)
Last possibility is that the battery discharged past the safety point, disconnecting it internally. You'd have to find a battery shop that could reset it, or buy a new battery. That almost never happens (the phone shuts off long before that point), but it's possible.
