Integrated communication-sensing-computing (ICSC) satellites, which integrate edge computing servers on Earth observation satellites to process collected data directly in orbit, are attracting growing attention. Nevertheless, some monitoring tasks involve sequential sub-tasks like target observation and movement prediction, leading to data dependencies. Moreover, the limited energy supply on satellites requires the sequential execution of sub-tasks. Therefore, inappropriate assignments can cause circular waiting among satellites, resulting in deadlocks. This paper formulates task offloading in ICSC satellites with data-dependent constraints as a mixed-integer linear programming (MILP) problem, aiming to minimize service latency and energy consumption simultaneously. Given the non-centrality of ICSC satellites, we propose a distributed deadlock-free task offloading (DDFTO) algorithm. DDFTO operates in parallel on each satellite, alternating between sub-task inclusion and consensus and sub-task removal until a common offloading assignment is reached. To avoid deadlocks arising from sub-task inclusion, we introduce the deadlock-free insertion mechanism (DFIM), which strategically restricts the insertion positions of sub-tasks based on interval relationships, ensuring deadlock-free assignments. Extensive experiments demonstrate the effectiveness of DFIM in avoiding deadlocks and show that the DDFTO algorithm outperforms benchmark algorithms in achieving deadlock-free offloading assignments.