Energy of Sinc function
The energy of $x(t)$ is given by

$$E_x=\int_{-\infty}^{\infty}x^2(t)dt=\int_{-\infty}^{\infty}\frac{\sin^2(\pi t)}{(\pi t)^2}dt\tag{1}$$

If we may assume that we know that $x(t)$ is the impulse response of an ideal low pass filter, the integral $(1)$ can be computed without using the Fourier transform and Parseval's theorem by noticing that it can be represented as a convolution evaluated at $t=0$:

$$E_x=(x\star x)(0)=\int_{-\infty}^{\infty}\frac{\sin(\pi\tau)}{\pi\tau}\frac{\sin(\pi(t-\tau))}{\pi(t-\tau)}d\tau{\huge|}_{t=0}\tag{2}$$

The convolution in $(2)$ can be seen as filtering an ideal low-pass signal with an ideal low-pass filter with the same cut-off frequency as the signal. Clearly, the filtering does not affect the signal, and the result of the convolution equals $x(t)$:

$$(x\star x)(t)=x(t)\tag{3}$$

And, consequently,

$$E_x=x(0)=1\tag{4}$$

(Note that the value of $x(t)$ at $t=0$ is defined as a limit.)