Plug the headphone in and out of the socket couple of times to turn the digital sound off.
System Preference > Sound
Make sure that the box Mute is not checked.
Choose the method for:
"Resetting SMC on portables with a battery you should not remove on your own".
Some sound settings are stored in PRAM.
Hope this helps.
The red light means the port is still live.
The cause is a little leaf switch that is pushed over by the headphone jack when you insert it. Sometimes these stick.
Try inserting and removing a jack a few (dozen) times.
If that doesn't free it you may attempt to tease it with a slim non-conducting tool (like a plastic toothpick). Ensure the Mac is not only shut down, but unplugged if you try this.
And be careful; the leaf is fragile and it's an expensive bit to get to and replace, in fact on some models it's directly on the logic board.