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First make sure the silent switch is not turned on. It is above the volume buttons on the left. If it is ON then switch it off.
If that didn't work, then we can reset your iPhone and see if it works or not. Press and hold down the Power button and Home button at the same time until it shows the Apple logo. When you see the Apple logo, release the buttons and let it boot.
Then go to Settings > General > Reset and tap Reset All Settings. This will reset some settings like ringtone settings, WiFi etc. The check if it is working or not.
If it still not working, then connect the headphone to the headphone port, take it out and repeat it for 5-10 times. This is to make sure it is not in headphones mode. Check now.
If it still not working, then we have to restore the iPhone from iTunes on your computer. Restoring will install a fresh OS on the iPhone. I will send you the instructions or I will remotely connect to your computer and restore it from your computer while you watch.
If you would like me to fix it for you, then you can accept the remote offer I sent you. If you would like instructions, then let me know and I will send them. You don't have to accept the remote offer if you only need instructions to fix it.