Could be a dead battery, could be a dead phone.
Cell phones and laptops now days use lithium-ion batteries, and they're only good for so long. They can only take so much abuse and be charged so many times. Eventually they lose the ability to hold a charge at all. Some are manufactured better than others and therefor last longer.
With that in mind, take the phone to a repair center and ask if they can test it with another battery. If the phone works with a new battery, then you know what the issue was and you can replace the battery.
If however the phone still doesn't work, it would indicate an issue with the phone itself. There's plenty of potential places the issue could occur, from hardware to software. If this is the case, it's best to either send the phone in for repairs or bid it farewell and buy yourself a new one.