Whatever the issue is with your broken cell phone, quite often there is a solution.
The first thing to do is to find out if your phone is still covered under a warranty and if the damage to your cell phone is covered under that warranty.
Some warranties will not cover issues considered abuse and neglect, and usually it will take a trip to your cell phone company to find out what that means exactly. If you have an issue such as a battery that no longer holds a charge, or just the typical wear and tear problems of owning a phone for longer than a year or two then your cell phone company should be able to replace or repair your phone for free if it is within the warranty, or perhaps you purchased an extended warranty.
If your cell phone is damaged because of an accident of yours and it is not covered under the warranty then you will need to try plan B. There are a few solutions to fix whatever the problem is with your phone, the first would be to try to repair your phone on your own. This would include going on a repair website and following instructions to fix whatever the issue is.
Websites such as YouTube or ifixit will offer video tutorials for step-by-step instructions, and ifixit will also include links to purchase parts or tools that you will need.
This will be easier to do if you are a little tech savvy and can follow the tutorials pretty well.
Another solution would be to take your phone to the company you bought it from which may be on the pricey side to repair though. There are many other stores that can fix your phone for probably a lot less such as Radio Shack, they offer either in-store repair or a drop off service where they repair your phone and return it to your door within 72 hours.
The Geek Squad at Best Buy is another phone fixing service, as is Cellairis where you can choose your location from anywhere in the U.S and you can go to them to service your phone.
There are some things you can do yourself to see if it fixes your problem such as putting your phone in dry rice to help it dry out if it has been dropped in water. Or if your battery is dying too quickly you can always just replace the battery and open your phone and do it yourself.
Before you bring in your phone to be fixed or you do it yourself, always remember to back up everything if possible before you start.