What happens to frequency domain components if I circular-shift the time domain samples?
If you circularly shift the array in the time domain, the DFT of the shifted sequence will have the same magnitudes in each bin, but the phases will be different, with $X[k]$ being transformed to $X[k]e^{jk\theta}$, 
$k = 0, 1, \ldots, N-1$, for a fixed value of $\theta$ that I will leave for
you to figure out.