The Cu2(1,4-diazacycloheptane)2Cl4 (CuHpCl) crystal is a molecular transition metal antiferromagnetic complex, whose magnetism has been a long-lasting issue. The outcome of a variety of experimental studies (on magnetic susceptibility, heat capacity, magnetization, spin gap and INS) reported many different J values depending on the fitting ladder model used. From all available experimental data, one can infer that CuHpCl is a very complex system with many competing microscopic magnetic JAB interactions that lead to its overall antiferromagnetic behavior. A first-principles bottom-up study of CuHpCl is thus necessary in order to fully disentangle its magnetism. Here we incorporate data from ab initio computations providing the magnitude of the JAB interactions to investigate the microscopic magnetic couplings in CuHpCl and, ultimately, to understand the macroscopic magnetic behavior of this crystal. Strikingly, the resulting magnetic topology can be pictured as a 3D network of interacting squared plaquette magnetic building blocks, which does not agree with the suggested ladder motif (with uniform rails) that arises from direct observation of the crystal packing. The computed magnetic susceptibility, heat capacity and magnetization data show good agreement with the experimental data. In spite of this agreement, only the calculated magnetization data are used to discriminate between the different spin regimes in CuHpCl, namely gapped singlet, partially polarized and fully polarized phases. Additional analysis of the magnetic wavefunction enables the conclusion that long-range spin correlation can be discarded as being responsible for the partially polarized phase, whose magnetic response is in fact due to the complex interplay of the magnetic moments in the 3D magnetic topology.