Have you tried powering it on while it's plugged in, without the battery inserted?
This would rule out the phone itself as being the issue.
See, cell phones and laptops nowadays use lithium-ion batteries and they're only good for so long. Also, some are made better than others. After a while they start to wear out and hold less and less of a charge until they're entirely useless. If your phone happened to come with a cheaply manufactured battery, this would occur much faster.
With that in mind, try my above suggestion. If the phone powers on without the battery inserted, while it's plugged into a power source - you know it's an issue with the battery, and need to replace it. If it still doesn't turn on, there may be internal damage in your phone.
Either way, you'll need to take it to a cell phone store/repair center for the new battery or phone repair. And as I said already, cheap batteries don't last. If you do get a new one, get a good one.