Take each of the following steps that you haven't already tried.
1. If anything is plugged into the audio-out (headphone) port, unplug it.
2. Select ▹ System Preferences ▹ Sound ▹ Output. Check the settings. The internal speakers should be selected as the output device, the Mute box should not be checked, and the volume slider should be at least halfway to the right.
3. You may need to darken the room for this step. Look inside the headphone port. If a red light is coming from the port, the internal switch is stuck in the position for digital output. You may be able to free it by inserting and removing a headphone mini-stereo jack of the proper size. Inserting any kind of tool in the port may cause damage that won't be covered by your warranty.
4. Boot in safe mode by holding down the shift key at the startup chime. It will take much longer than usual. You don't have to log in; just reboot as usual (without holding any keys) when the login screen appears. (Note: If FileVault is enabled under OS X 10.7 or later, or if a firmware password is set, you can’t boot in safe mode.)
5. Reset the PRAM. Shut down completely, then start up while holding the key combination command-option-P-R. Release the keys when the machine restarts automatically.
6. Make a "Genius" appointment at an Apple Store.
Back up all data on the internal drive(s) before you hand over your computer to anyone. If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to bare metal from any of them.) Don’t erase the OS X 10.7 or later recovery partition, if present.
*An SSD doesn't need to be zeroed.
