Thirteen new 4,7-disubstituted pyrimido[4,5-d]pyrimidines were synthesized via a straightforward methodology starting from thiourea. The anti-proliferative activity of these compounds was evaluated across a diverse panel of eight cancer cell lines, with derivatives 7d and 7h showing efficacy against several hematological cancer types. Furthermore, all compounds were assessed for their antiviral potency against a panel of viruses. Compounds featuring a cyclopropylamino group and an aminoindane moiety exhibited remarkable efficacy against human coronavirus 229E (HCoV-229E). These findings highlight the pyrimidino[4,5-d]pyrimidine scaffold as an interesting framework for the design of novel antiviral agents against HCoVs, with compounds 7a, 7b, and 7f emerging as strong candidates for further investigation.