Peek in the digital audio port. Can you see a red light glowing?
If so, a slightly out-of-spec analog audio plug has likely jammed the digital port (tighter specs) in the MUTE position. Apple's official fix is to replace the logic board, but most people area able to fix it by putting a plug in the port and GENTLY wiggling it in the horizontal plane.
I've found with both my MBP and a circa 2003 PowerBook G4 that most analog plugs will deliver proper output and stereo separation long before the stop shoulder on the plug touches the case. The plug is held firmly enough to stay put for normal usage. It's inserting the plug "to the hilt," so to speak, that jams the MUTE contact.
I've taken to putting on headphones or turning on external speakers BEFORE plugging them into my notebooks. I insert the plug slowly until I hear proper sound, then stop pushing. No jams since adopting that procedure.
If there is no red light, I'd head for the Apple Store or AASP. Although some say an SMC reset will fix the muting in the absence of the red light clue, I'd let Apple work on a new computer.
I'll try so get a picture later today of what mine looks like with the plug in a functional position. I recall the stop shoulder being between 1/16- and 1/8-inch from touching the case on either notebook model I have.
Sorry about that. It's the headphone port.
Instructions on the SMC reset are here:
Scroll down to find the link for specific product groups. If your MBP does not have a user-serviceable battery, you'd use this one: