If you're beyond the 90-day free telephone support period and don't have AppleCare on the iPhone, then yes, Apple will charge you for assistance unless the problems turns out to be one that would be covered under the warranty. But if you have an Apple Store in your area, you can make an appointment at the Genius Bar there and they will help you at no charge.
For assistance here, without any information other than "won't work" it's difficult to offer much in the way of useful suggestions. All I can suggest is that you try the usual steps: restart, reset, restore.
If you try restoring from a backup and that doesn't fix the problem, try restoring to factory settings and, if the problem goes away, then synching your apps. You'll lose the app data and settings, but if the problem is due to a corrupt cache or settings file, that should cure it.
If none of that helps, your device may have developed a hardware fault and will need to be take or sent to Apple.