We present a new method for probing the physical conditions and metal enrichment of the Intergalactic Medium: the composite spectrum of Ly-alpha forest absorbers. We apply this technique to a sample of 9480 Ly-alpha absorbers with redshift 2 < z < 3.5 identified in the spectra of 13,279 high-redshift quasars from the Sloan Digital Sky Survey (SDSS) Fifth Data Release (DR5). Absorbers are selected as local minima in the spectra with 2.4 < tau_Ly-alpha < 4.0; at SDSS resolution (~ 150km/s FWHM), these absorbers are blends of systems that are individually weaker. In the stacked spectra we detect seven Lyman-series lines and metal lines of O VI, N V, C IV, C III, Si IV, C II, Al II, Si II, Fe II, Mg II, and O I. Many of these lines have peak optical depths of < 0.02, but they are nonetheless detected at high statistical significance. Modeling the Lyman-series measurements implies that our selected systems have total H I column densities N_HI ~ 10^15.4cm-2. Assuming typical physical conditions rho / = 10, T = 10^4 - 10^4.5 K, and [Fe/H]= -2 yields reasonable agreement with the line strengths of high-ionization species, but it underpredicts the low-ionization species by two orders of magnitude or more. This discrepancy suggests that the low ionization lines arise in dense, cool, metal-rich clumps, present in some absorption systems.