Could be a few things, battery, charging port, or HDD. Possibly the Logic Board but there's things you can try before getting to the stage. If you have anywhere local that'll look at it I'd book it in though as it'll save you hassle down the road, at least diagnose it for you and you can go from there. But there'll be a lot of questions I'm afraid!
Is it all original stuff in there, have you changed any components? Using official chargers? Is the MagSafe port clean, dirt could be interfering with the charging. Is it actually charging do you know?
The HDD could have become corrupted and is failing to boot. Was there anything suspicious going on before you experienced these problems? Did it just all of a sudden happen or were there a few times something happened before?
The battery could have failed somewhere, it is old enough to question it. Do you know the health of the battery? Have you had it since 2012? Have you used it mainly on battery in that time or anything? It's unlikely, as it should bypass the battery and run directly from a power source if it had failed. However something could possible go wrong and it's getting confused by trying to run from a dead battery.
Are you comfortable opening it up? You could disconnect the battery entirely from the machine (And also see if there's any obvious issues, could even be a build up of dust so give it a good clean), and try running it directly from a power source. This would eliminate this problem.
If you have a spare HDD that would fit, you could try removing the original HDD and fitting the other one, this would again eliminate that potential issue.
So I'd give it a really good clean and check those things if possible as it wouldn't take long. If all that fails then it's likely to be a problem with the Logic Board, in which case you may I'm afraid be better off buying a new computer. However, it could also be something simple like a blown resister which is where I'd advice you to take it to a repair centre (Apple possibly although they wouldn't repair it, they'd simply replace), as you might get away with a small and relatively cheap solution.
Hope that helps and good luck!