We measured the concentrations of noble gases in 32 ordinary chondrites from the Dar al Gani (DaG) region, Libya, as well as concentrations of the cosmogenic radionuclides C-14, Be-10, Al-26, Cl-36, and Ca-41 in 18 of these samples. Although the trapped noble gases in five DaG samples show ratios typical of solar or planetary gases, in all other DaG samples, they are dominated by atmospheric contamination, which increases with the degree of weathering. Cosmic ray exposure (CRE) ages of DaG chondrites range from similar to1 Myr to 53 Myr. The CRE age distribution of 10 DaG L chondrites shows a cluster around 40 Myr due to four members of a large L6 chondrite shower. The CRE age distribution of 19 DaG H chondrites shows only three ages coinciding with the main H chondrite peak at similar to7 Myr, while seven ages are <5 Myr. Two of these H chondrites with short CRE ages (DaG 904 and 908) show evidence of a complex exposure history. Five of the H chondrites show evidence of high shielding conditions, including low Ne-22/Ne-21 ratios and large contributions of neutron-capture Cl-36 and Ca-41. These samples represent fragments of two or more large pre-atmospheric objects, which supports the hypothesis that the high H/L chondrite ratio at DaG is due to one or more large unrecognized showers. The C-14 concentrations correspond to terrestrial ages <35 kyr, similar to terrestrial ages of chondrites from other regions in the Sahara but younger than two DaG achondrites. Despite the loss of cosmogenic Cl-36 and Ca-41 during oxidation of metal and troilite, concentrations of Cl-36 and Ca-41 in the silicates are also consistent with C-14 ages <35 kyr. The only exception is DaG 343 (H4), which has a Ca-41 terrestrial age of 150 +/- 40 kyr. This old age shows that not only iron meteorites and achondrites but also chondrites can survive the hot desert environment for more than 50 kyr. A possible explanation is that older meteorites were covered by soils during wetter periods and were recently exhumed by removal of these soils due to deflation during more and periods, such as the current one, which started similar to 3000 years ago. Finally, based on the Al-26/Ne-21 and Be-10/Ne-21 systematics in 16 DaG meteorites, we derived more reliable estimates of the Be-10/Ne-21 production rate ratio, which seems more sensitive to shielding than was predicted by the semi-empirical model of Graf et al. (1990) but less sensitive than was predicted by the purely physical model of Leya et al. (2000).