In this research, an innovative and clean shipboard Sustainable Hybrid Energy and Carbon Capture System (SHECCS) is proposed, addressing the energy demand of a ship in both sailing and mooring modes. To comprehensively utilize renewable energy, LNG cooling energy, and ship waste heat, the SHECCS integrates multiple subsystems, including the Carbon Capture Subsystem, Liquefied CO2 Subsystem, Carnot Battery Subsystem, Multi-Effect Distillation Desalination Subsystem, Ejector Refrigeration Cycle Subsystem, Organic Rankine Cycle Subsystem, and Photovoltaic Panels. Together, these subsystems enable carbon capture and liquefaction, energy storage, distilled water production, refrigeration, and power generation for ships. The system's performance is evaluated using energy, exergy, environmental, and economic (4 E) assessments. The effects of the split ratio, direct normal irradiance, liquid-to-gas ratio, and exhaust gas flow rate on the system are investigated. Additionally, considering the intermittency and fluctuation of solar resources, the impact of storage duration on the system is also analyzed. Under the design conditions, the system's distilled water production and cooling capacity are 21.710 m3/day and 121.800 kW, respectively. The optimization of the system uses all-day energy efficiency, all-day primary energy ratio, and payback period as objectives. The results indicate that the system achieves an all-day energy efficiency of 39.470% and an all-day exergy efficiency of 40.300%. Regarding the environmental analysis, the all-day primary energy ratio and Energy Efficiency Design Index are 4.511 and 7.705 G/t & sdot;nmile, respectively. The system has a payback period of 13.420 years and a total investment cost of $6.139 x 106.