This could be due to four different issues.. Your battery may be faulty, and unable to be charged. In this case, you will need to buy a new battery or have it replaced under warranty. Before you replace the battery, you should first ensure the charger is functioning. To find if the charger functioning, you may use a different charger on your phone, or use the same charger on another phone. Rule this out before purchasing a new battery as batteries are much more expensive than chargers. Similarly, chargers are also covered under warranty. Thirdly, your phone may be faulty. Faulty software may be stopping the phone from switching on. Finally, if you have liquid or physically damaged the phone, this may cause it to malfunction. Hopefully this is not the case, as it won't be covered under warranty. In terms of warranty, in Australia for the phone company I work for, battery and chargers have a 6 month warranty and the phone has a 12 month warranty which covers only factory faults (not liquid or physical damage). To troublshoot, try pulling the battery out and putting it back in, then turning the phone on. This solves these sort of issues alot of the time. Hope that helps :)
I may or may not be able to repair a battery charger depending on what is wrong with it. I would check the fuse and the wiring. If it is not something visible, then the parts will probably cost me more than a new battery charger and I will throw it away and get a new one.
new battery or new charger
There is no fool proof way. Get a new battery if putting it on a slow charger does not work.
You will destroy the battery and be buying a new one.
No it doesn't come with a battery charger, but you can one for cheap price from amazon.com. It is around 10$ new or 5$ used. You can also try Walmart.
You can buy a battery charger at any used or new electronics and hardware store. You can also purchase a charger online. Places like Best Buy and Future Shop would be the best.
Some car battery charges will not charge a completely dead battery. You need to find a type of battery charger that is designed to charge a completely dead battery. You can get around this by hooking a car with a working battery up to the dead battery with jumper cables. The alternator/charging system of the car with the good battery will charge the dead battery. Leave them connected for about 30 min, then disconnect and try to use the battery charger again. If it still won't charge, hook it up to the car with the good battery for a longer period of time.
You might need a new charger or battery.
I would look online at Amazon. You should be able to buy a charger for a low price.
Try the charger again at a friends house, if that doesn't work contact the supplier for a warranty claim, or if out of warranty you may have to purchase a new one. Many different kinds of chargers can be found on Ebay for reasonable prices.
Oh, that seems you need to get a new battery to check out.