I had exactly the same problem on my latop ASUS F3Ke: the sound from its internal speakers works fine, but when I plug in headphones - no sound at all. I brought the laptop to the ASUS service centre - and the solution was TRIVIAL (but not easy to guess

):
When the laptop just starts up:
- press F2 to get into BIOS.
- go to the menu "Advanced".
- in the item "Play POST sound" select: Yes.
- in the next item "Speaker volume" select: 0.
- go to the menu "Exit" and select "Save changes and exit".
The laptop will restart normally.
Note: in your model, the menu items may differ slightly. And do NOT change anything else in BIOS: it is a fine-tuned place, for professionals only!
Explanaition: when the laptop starts up, it shows a logo ASUS and plays a short melody. It's usually annoying, especially if you are in a quiet room (i.e., lecture), and people usually turn it off. In BIOS, the item "Play POST sound" turns on/off this melody (You will see a hint there: "Select Yes if you need to play POST sound on boot"). BUT (!!!) as a side effect (I assume it's a BUG), it turns off the sound from headphones jack completely!! The compromise was easy: turn ON this melody (i.e., set "Play POST sound" into Yes), but reduce its volume to 0 (this does NOT affect the volume of the sound in headphones or internal speakers! only for the start-up melody). Then you have NO melody at the start-up, but get the headphones working normally.
Good luck!
