We present the results of a large search for intrinsic HI 21 cm and OH 18 cm absorption in 145 compact radio sources in the redshift range 0.02< z <3.8 with the Green Bank Telescope. We re-detect HI 21 cm absorption toward six known absorption systems but detect no new HI or OH absorption in 102 interference-free sources... 79 sources have not previously been observed for HI 21 cm absorption. We recover a mean optical depth limit of $\tau_{3\sigma}<0.023$ for all the non-detections in the survey. Our results do not support the high intrinsic absorption rates found by previous studies in compact radio sources at low redshift. Our results do, however, support the hypothesis proposed by Curran et al. (2008) that high ultraviolet (UV) luminosity active galactic nuclei (AGN) do not show intrinsic HI 21 cm absorption, confirming a threshold of $L_{\rm UV} = 10^{23}$ W Hz$^{-1}$, above which our intrinsic absorption fraction is zero (54 sources). The exact nature of the UV luminosity effect on HI absorption systems remains ambiguous. We additionally find no statistical correlation between the 1.4 GHz radio luminosity or the source size and the 21~cm absorption detection rate. We attribute the lack of intrinsic absorption in our survey to the UV luminosity effect caused by an optical selection bias and a decreased column density sensitivity with increasing redshift due to lower radio continuum flux densities, high radio frequency interference, and higher telescope system temperatures at low frequencies. (read more)