You probably already found about free internet kiosks in Sydney airport (unfortunately only in international T1 terminal). Just checked-in, it is almost two hours until your boarding, so you have more then enough time check your email, update status on facebook. But what is happening? Why it is not possible to enter password into box ? Don’t know what is happening, but best way pass this, just press on “Login”  button without any password entered.
Will be shown next window with error message of course: “Incorrect Email/Password Combination
Facebook passwords are case sensitive. Please check your CAPS lock key. You can reset your password here.”
Surprisingly in this window it is possible enter password into  box.
Then press “Login” button  and you are in.