I have a Nikon D300S. I have tried using the self-timer; I have it set. However, I push the shutter release button halfway and it takes the picture instead of starting the timer.
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Have you set the release mode to self timer? (ring at the bottom of the left hand knob that usually says S or CL or CH in the cutout at the back, with an unlock button at front left of the knob) - The self timer symbol is the last one before MUp.
If you've been setting the delay in the menu from the rear LCD, that just sets how long the delay is when in self timer mode - it doesn't put you into self timer mode. For that, you have to change the release mode setting as above.
If you have set the release mode to self timer, it may be worth checking what delay you've got it set to in the LCD settings menu; you can set how many seconds it waits before taking the picture. I can't remember if it lets you set the delay down to zero, but you can certainly set it to something short, so worth checking to see if that might be another possible cause.