DNA is a promising medium for digital information storage for its exceptional density and durability. While prior studies advanced coding theory, workflow design, and simulation tools, challenges such as synthesis costs, sequencing errors, and biological constraints (GC-content imbalance, homopolymers) limit practical deployment. To address this, our framework draws from quantum parallelism concepts to enhance encoding diversity and resilience, integrating biologically informed constraints with deep learning to enhance error mitigation in DNA storage. NeuroDNAAI encodes binary data streams into symbolic DNA sequences, transmits them through a noisy channel with substitutions, insertions, and deletions, and reconstructs them with high fidelity. Our results show that traditional prompting or rule-based schemes fail to adapt effectively to realistic noise, whereas NeuroDNAAI achieves superior accuracy. Experiments on benchmark datasets demonstrate low bit error rates for both text and images. By unifying theory, workflow, and simulation into one pipeline, NeuroDNAAI enables scalable, biologically valid archival DNA storage