Actually, Quillen's proof did contain a fantastic new idea : Quillen patching.
It states that if P$P$ is a fg projective R[t]$R[t]$-module then the set of all f in R$R$, such that (for localizations at the multiplicative systems {1,f,f^2,...}) P_f$ \left\{ 1,f,f^2,... \right\}$ $P_f$ is extended from R_f$R_f$ (that is P_f = Q \otimes_{R_f} R_f[t]$P_f = Q \otimes_{R_f} R_f[t]$ for a projective R_f$R_f$-module Q$Q$, is an ideal of R$R$.
Apply this to R=k[x1,...,xd]$R=\mathbb k[x_1,...,x_d]$ then the localization of P$P$ at the set of all monic polynomials in R[t]$R[t]$ is a projective k(t)[x0,...,xd]$k(t)[x_0,...,x_d]$ module whence free by induction. But then P_g$P_g$ is free for some monic poly g$g$ in t$t$.
Now take a maximal ideal m$\mathfrak m$ of R$R$ and consider the extension Pm$P\mathfrak m$ of P$P$ to R_m[t]$R_\mathfrak{m}[t]$ (the localization at R-m$\mathfrak m$). Because (Pm)_g$(P\mathfrak m)_g$ is a free (R_m[t])_g$(R_\mathfrak{m}[t])_g$ module it follows from Horrocks result that Pm$P\mathfrak m$ is a free R_m[t]$R_\mathfrak{m}[t]$-module and extended from R_m$R_m$. Whence the Quillen-ideal for P$P$ equals R$R$. Serre's conjecture follows by considering 1$1$ and induction.
