Cause for normal audio over speaker but only static over headphones?

Hi,

my 1st gen iPhone still works like a charm, but when I plug in headphones (I tried different ones) I only hear a buzzing sound. This noise is independent of any action (i.e. play/stop music, receiving a call). Although the iPhone seems to detect the headphones, because it turns of the speaker.

As a blind shot I replaced the headphone jack with the matching part, but the problem stays the same.

It would be great if anyone could give me a hint, where I could look next.

Thomas