I would first try mountainbikermike's suggestion and rub the battery contacts with a pencil eraser. If the battery only lasts less than 6 hours on a full charge, then you should get a new one.
Don't do a factory data reset until you have saved everything you want to save (pictures, documents, texts, etc). There are several ways to save what you want to save. A factory data reset will erase everything on your phone so that it is like new. When you are done, you will have to set up your phone with your email and password the same as you did when you first activated it.
It will take a few hours to save everything you want, do the FDR and then restore everything back on your phone again, so allow yourself plenty of time.
Don't do a factory data reset until you are confident that you have everything saved first.
Before doing an FDR, go into your phone settings, go to "backup and reset," turn on "back up my data." This will back up only some of your data but not all of it.
To save everything else, you can follow the step by step instructions here,
Getting the most success upgrading to ICS from GB
(This is an old post but still works).
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