Find $\int_{-\infty}^{\infty} \frac{\sin^4{k}}{k^4}dk$ using Parseval's Theorem

Question

I'm having a little trouble with this one. So far I've found that $$g(k) = \sqrt{\frac{2}{\pi}}\frac{\sin{k}}{k}$$ when $f(x) = 1, |x| < 1$ and $0$ elsewhere. I've also found the convolution $(f*f)(x)$ is $$\frac{1}{\sqrt{2\pi}}\begin{cases}0&x\le -2\\\\\int_{-1}^{x+1}(1)\,dx=(x+2)&-2<x<0\\\\\int_{x-1}^1(1)\,dx=2-x&0\le x<2\\\\0&x\ge 2\end{cases}$$ And the Fourier transform of this is $$\frac{2}{\pi}\frac{\sin^2{k}}{k^2}$$ I'm sure that from here the answer is quite simple, however I'm having a hard time figuring out the last step. Any help is appreciated.