We present intermediate-resolution spectra of six QSOs exhibiting seven Lyalpha absorption troughs that are candidates for damped Lyalpha absorption lines. The candidates are selected from low-resolution spectra comprising the Lick survey for damped Lyalpha systems of Wolfe et al. (1986). The damping hypothesis is checked by fitting the Lyalpha troughs with Voigt damping profiles, and by comparing the velocity profiles of Lyalpha and associated metal-line transitions. We find that six of the seven candidates are in fact damped Lyalpha lines. All six damped Lyalpha lines arise in redshift systems with H I column densities N(H I) greater-than-or-equal-to 2 x 10(20) cm-2. In Paper III of this series (Turnshek et al. 1989) we confirmed another six damped Lyalpha absorption systems from the Lick survey with N(H I) greater-than-or-equal-to 2 x 10(20) cm-2. Accounting for three independent confirmations by other workers, we conclude that the Lick sample contains at least 15 damped Lyalpha systems with N(H I) greater-than-or-equal-to 2 x 10(20) cm - 2. We investigate the metal content of the confirmed damped systems by examining the metal-line velocity profiles, and by performing curve-of-growth analyses for four of the six confirmed damped systems. We find that the low-ionization lines associated with the z(metals) = 2.0399 damped system toward Q0458-020 have velocity widths up to 10 times wider than the width of the 21 cm absorption feature found at the same redshift. Since the 21 cm absorption arises in a low velocity dispersion layer of H I that extends more than 8 h-1 kpc transverse to the line of sight, the H I absorption cannot arise from the same clouds responsible for the bulk of the metal-line absorption. This is strong evidence for a two-component model consisting of high column density '' quiescent '' gas which gives rise to damped Lyalpha and 21 cm absorption, and low column density ''turbulent'' gas which dominates the equivalent widths of saturated metal lines. Our curve-of-growth analysis is based on a single Gaussian velocity component. The result of model fitting with least-squares minimization techniques is that the FWHM of the Gaussian is significantly less than the widths of resolved low-ionization metal lines. We interpret this to mean that significant gaps in velocity space exist between the narrow velocity components comprising the '' turbulent '' gas. A similar result is found for the z(metals) = 2.1386 absorber toward Q2136 + 141, the redshift system that is not confirmed as a damped Lyalpha system. The curve-of-growth analysis also reveals that the ionic column densities of the ''turbulent'' gas resembles the column densities of halo gas found along the sight lines to the Magellanic clouds.