We investigate the production of a heavy charged Higgs boson at hadron colliders within the context of the MSSM. A detailed study is performed for all important production modes and basic background processes for the tb signature. In our analysis we include effects of initial and final state showering, hadronization, and principal detector effects. For the signal production rate we include the leading SUSY quantum effects at high tan βm_t/m_b. Based on the obtained efficiencies for the signal and background we estimate the discovery and exclusion mass limits of the charged Higgs boson at high values of tan β. At the upgraded Tevatron the discovery of a heavy charged Higgs boson (M_H^±200 GeV) is impossible for the tree-level cross-section values. However, if QCD and SUSY effects happen to reinforce mutually, there are indeed regions of the MSSM parameter space which could provide 3σ evidence and, at best, 5σ charged Higgs boson discovery at the Tevatron for masses M_H^±300 GeV and M_H^±250 GeV, respectively, even assuming squark and gluino masses in the (500−1000) GeV range. On the other hand, at the LHC one can discover a H^± as heavy as 1 TeV at the canonical confidence level of 5σ; or else exclude its existence at 95% C.L. up to masses ~ 1.5 TeV. Again the presence of SUSY quantum effects can be very important here as they may shift the LHC limits by a few hundred GeV.