The synthesis and characterization of three new platinum complexes, with 3,5-diacetyl-1,2,4-triazole bis(4-N-isopropylthiosemicarbazone) as a ligand, are reported. The specific conditions under which solvent coordination takes place are reported and the X-ray structure of the complex with one solvent molecule of dimethyl sulfoxide is resolved. Analysis of the reactivity of these platinum compounds aids in finding the best solution profile for biological investigations. Then, the interactions of the complexes with biological models, such as calf-thymus DNA, are studied by using UV spectroscopy and tracking the changes in electrophoretic mobility produced in the supercoiled plasmid DNA model. Initial screening of these potential antitumoral compounds indicates possible selective antitumoral action.