Hi,
Internet has become the gateway for everything you do nowadays. If your moblie doesn't boot up and you think it is because the battery is dead, you may certainly be wrong. Firstly samsung's orginal batteries are of high qualities the chance that it dies in only 6teen months is very odd. I will give you the details for your question, but I ill recommend that you check for the following first:
1. You phone might have been hard bricked. In such cases, your phone appears to be no more than a dummy model. It wont boot up, nor charge. This generally happens because your software has totally been crashed. Luckily, Samsung phones call be easily recovered from a hard brick. Try taking your phone to a service centre or check online by typing your "phone's model" and then "hard bricked", and luckily you will get it resolved.
2. Check if your motherboard or anyother hardware is alright. Go to a nearby electronic store and ask them to check your phone by connecting the contact points with some sort of car batteries (not car batteries exactly, but they are big enough and contain readings like voltage and current; You might have seend them in your science experiments.) of low voltage. Try rebooting your phone. The hardware is gone, if it doesn't boot up.
Now, if you are sure you that your battery is the fault, i will recommend that you buy third party batteries. Their quality differs only by a margin from Samsung but they offer more mAh and are quite offordable. Google for your device to find out the best third party battery