No audio out with headphones

When I plug a headphone into my Nexus' audio port, the headphones simply don't play any sounds or music. The device seems to detect them, because the built-in sound output stops working. I tried it with another headphone and it didn't work either. There is no error log output. It really sucks, because I can't hear any music. How can I solve it? (Galaxy Nexus with stock Jelly Bean)