This perspective introduces the Intracellular Biological Perceptron (IBP), an original theoretical framework proposing neuronal-inspired synthetic gene circuits for weighted, multi-input intracellular cancer classification. Unlike existing Boolean AND-gate approaches, the IBP architecture mimics artificial neural network computation — integrating cancer-associated biomarkers (oncogenic microRNAs, transcription factor activities, metabolic flux indicators) as weighted inputs into a graded, probabilistic cancer classification output. A multi-layer extension — the Biological Deep Network (BDN) — is proposed for intracellular cancer staging. Applications in glioblastoma, pancreatic adenocarcinoma, and non-small cell lung cancer are discussed, alongside a four-phase experimental validation roadmap.