Computer Not Detecting Headphones?.
Good find DSTM, follow that and I think DSTM means the first on the left "Top Solutions" click on that first then go to the second page, there are several audio fixes listed there.
If however there is nothing there that works, it may just be the headphone jack socket broken. Is it regularly used, or once the headphones are plugged in they stay there? If regularly used, then the constant plugging in and out may have snapped the contacts, so considering it is only a few months old, it should still be under warranty for hardware repairs such as that. If so send or take it back, the socket should have lasted longer than it has.
Nev.