As the supply network for community-based elderly care services expands, the research focus shifts from mere service availability to computationally modeling who can access and utilize services effectively. Existing studies often consider accessibility as spatial distance or economic cost and equity as simple resource allocation, limiting insights into cumulative disadvantages faced by older adults with low income, digital barriers, or limited family support. Based on data from 3,800 community elder care sites across 20 U.S. metropolitan areas, individual survey data from 6,240 older adults, and community socioeconomic indicators, this study constructs a computational five-stage accessibility chain model: “Information Accessibility—Eligibility Determination—Process Accessibility—Service Availability—Outcome Attainability.”The study integrates heterogeneous data encoding, adaptive spatial accessibility computation, stage-aware vulnerability representation, and hierarchical modeling. Two-Step Floating Contour Analysis (2SFCA), stage-coupled logit modeling, and deep embedded clustering are applied to stratify risk and optimize service access prediction. A cross-vulnerability index, combining six factors—age, income, cognition, language proficiency, family support, and digital access—is incorporated into the model to quantify cumulative impacts across stages.Preliminary results indicate that inequalities do not primarily arise from geographic proximity but accumulate during intermediate phases of information identification, eligibility determination, and process navigation. Digital vulnerability and lack of family support remain major limiting factors even after controlling for spatial accessibility, demonstrating the effectiveness of stage-aware, computationally optimized modeling. This paper proposes an integrated “accessibility chain–intersectional vulnerability” computational framework, advancing service equity from outcome equity to process and transformational equity, and providing a technology-driven foundation for targeted service allocation, navigation system optimization, and identification of high-risk groups in community-based elderly care.