It has been pointed out recently that the presence of dilaton field in the early Universe can dilute the neutralino dark matter (DM) abundance, if Universe is not radiation dominated at DM decoupling, due to its dissipative-like coupling to DM. In this scenario two basic mechanisms compete, the modified Hubble expansion rate tending to increase the relic density and a dissipative force that tends to decrease it. The net effect can lead to an overall dramatic decrease of the predicted relic abundance, sometimes by amounts of the order of $ \mathcal{O}\left( {{{10}^2}} \right) $ or so. This feature is rather generic, independent of any particular assumption on the underlying string dynamics, provided dilaton dominates at early eras after the end of inflation but before Big Bang Nucleosynthesis (BBN). The latter ensures that BBN is not upset by the presence of the dilaton. In this paper, within the context of such a scenario, we study the phenomenology of the constrained minimal supersymmetric model (CMSSM) by taking into account all recent experimental constraints, including those from the LHC searches. We find that the allowed parameter space is greatly enlarged and includes regions that are beyond the reach of LHC. The allowed regions are compatible with Direct Dark Matter searches since the small neutralino annihilation rates, that are now in accord with the cosmological data on the relic density, imply small neutralino-nucleon cross sections below the sensitivities of the Direct Dark Matter experiments. It is also important that the new cosmologically accepted regions are compatible with Higgs boson masses larger than 120 GeV, as it is indicated from the LHC experimental data. The smaller annihilation cross sections needed to explain WMAP data require that the detector performances of current and planned indirect DM search experiments through γ − rays should be greatly improved in order to probe the CMSSM regions.