This paper explores the concept of Casimir-biased nanoelectromechanical systems (NEMS) for ultra-low-energy mechanical computation and memory. By leveraging Casimir forces as passive biasing elements, switching energy requirements may be reduced while enabling persistent mechanical memory states. The paper presents conceptual architectures, first-order scaling relationships, potential benefits, engineering limitations, and possible applications in extreme-environment computing systems where conventional electronics face significant challenges. While the analysis is conceptual and requires experimental validation, the approach suggests a potential pathway toward resilient, energy-efficient mechanical information processing systems.