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There are two possible reasons behind this problem.
1) On the left side there is a switch above the volume buttons. If the orange is visible on that switch, it is set to silent. Please, switch it the other way to disable the silent mode.
Test the ringer now. If and only if the problem still exists, continue below.
2) From the home screen, tap Settings > General > Accessibility > Assistive Touch and turn it on. Now you will see a white circle on the screen, tap that circle > device > Tap Mute/Unmute. Now you can go back and turn the Assistive Touch off.
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