Example 14 If $x^{3}+x^{2}+x+1=0$, then the value of $y=$ $x^{97}+x^{98}+\cdots+x^{103}$ is ( ).
(A) -1
(B) 0
(C) 1
(D) 2
Given: $\because x^{3}+x^{2}+x+1=0$, then from
$$
x^{4}-1=(x-1)\left(1+x+x^{2}+x^{3}\right)
$$

we get $x^{4}=1$.
$$
\begin{aligned}
\therefore \text { the original expression }= & x^{97}\left(1+x+x^{2}+x^{3}\right) \\
& +x^{100}\left(x+x^{2}+x^{3}\right) \\
= & x^{97} \times 0+\left(x^{4}\right)^{25} \times(-1) \\
= & -1 .
\end{aligned}
$$

Therefore, the answer is (A).