We present high-resolution (3.5 km s(-1)) Goddard High Resolution Spectrograph (GHRS) measurements of the Mg II, Si II, Cr II, Fe II, and Zn II lines toward HD 167756, a low-latitude halo star at a distance of 4 kpc in the direction l = 351 degrees.5, b = -12 degrees.3 and at a Galactic altitude of z = -0.85 kpc. Supplemental Na I, Ca II, and HI data are also presented for comparison with the UV lines. Our analysis centers on converting the observed absorption-line data into measures of the apparent column density per unit velocity, N-a(v), over the velocity range -25 less than or equal to v(1st) < 30 km s(-1) for each species observed. We use these N-a(v) profiles to construct logarithmic abundance ratios of Mg II, Si II, Cr II, Fe II, and Ca II relative to Zn II, normalized to solar abundances, as a function of velocity. Compared to Zn, these species show an underabundance relative to their solar values, with the largest underabundances occurring in the v(1st) approximate to 5 km s(-1) component(s), for which we find logarithmic abundances A(Si/Zn) > -0.38, A(Mg/Zn) = -0.82, A(Cr/Zn) = -1.18, and A(Fe/Zn) > -1.40 dex. We show that ionization effects, abundance gradients, or intrinsic abundance variability cannot be significant sources for the underabundances observed. The most likely explanation is gas phase depletion of elements onto dust grains. Comparisons with the gas phase abundances along other diffuse, warm gas sight lines, like the halo sight line to HD 93521, support this interpretation as do the derived physical properties of the sight line. We find that the sight line to HD 167756 is characterized by warm, low-density gas interspersed with several zones of higher density, cooler gas. The gas temperatures of the neutral regions containing the observed dominant ion absorption are probably between 1000 and 5000 K (our analysis includes temperatures as high as 7000 K if Na is undepleted), although some clouds, particularly those detected in Na I, may have T < 1000 K. The electron densities determined from ionization balance considerations are 0.02 < n(e) < 0.20 cm(-3). This range, more typical of denser molecule-bearing clouds, probably signifies mixing between strictly neutral gas and gas containing H+. Differences arising in the physical properties like temperature and n, determined from species such as Na I or Zn II and Ca II can be explained if some of the low ion absorption occurs in transition regions between neutral and ionized gas. Structured absorption seen in more highly ionized species like Si IV and C IV favors the existence of such regions along the sight line.