^That.
Try finding someone with the same phone as you, and put their battery in your phone. If it works, you know it's the battery. Lithium-ion batteries are only good for so long and can only take so much abuse or be charged so many times. Eventually they lose the ability to hold a charge at all. Some are made better than others and therefor they will last for a longer period of time before needing to be replaced - your phone may have come with a cheaply manufactured battery and has since worn out.
If the phone still doesn't work with a friends battery inserted, it would indicate an issue with the phone. It would most likely be a shorted or broken circuit in this scenario - probably caused by either water damage or being dropped one too many times and a wire inside has come loose. In this case you'll need to have the phone professionally repaired at a service center.
You can always double check by putting your battery in their phone, and if it causes the same issues on their device as it does on yours, then you can be 100% certain.