Do the sliders move when you use the TAT?
Version of LR and OS?
Is the sky perfectly white? Then the HSL sliders and targeeted adjustment tool will have no effect at all.
The sliders move but there is no difference showing in the pic. Using LR 5 and Windows 7.
As dj already asked: What's the color of the sky?
Which sliders do move?
Is it jpg or RAW, can you post a screenshot?