The cork itself is not visible when the headjoint is fully assembled. The cork assembly consists of three parts: the threaded stem/endplate, the cork itself, and the stem disc. When the headjoint and cork are fully assembled, the cork is situated between the stem/endplate and the stem disc and cannot be seen when looking in either end of the headjoint.
This video shows it all:
http://www.youtube.com/watch?v=H1zhtsUqDls
Is the crown and headjoint cork assembly missing or have you removed the crown and cork assembly to verify that the cork is missing from the assembly?
If there is no cork on the stem, it will leak air. This will prevent the flute from playing properly. Without the cork or cork assembly, the flute can make sounds, but it will not be correct the sounds. Every flute needs the cork to provide an airtight seal so that it plays correctly. If it is missing, you should take it to a repair shop to get a cork installed.
<Added>I just saw you posting about "Octave note help!". If your flute headjoint cork is missing, that could explain your problems!!!