The red light is the digital output. It should only be on when something is plugged into the headphone jack.
There's a switch in the headphone jack which detects when something is plugged in. This sometimes gets stuck. Plugging/unplugging/jiggling a headphone plug in there sometimes gets it unstuck.
No actually it is a hardware issue as stated by tele_player above. Most jacks of this type have a similar switch to disconnect one type of output while enabling another.