Apoptosis and hypertrophy of cardiomyocytes are the primary causes of heart failure and are known to be regulated by complex interactions in the underlying intracellular signaling network. Previous experimental studies were successful in identifying some key signaling components, but most of the findings were confined to particular experimental conditions corresponding to specific cellular contexts. A question then arises as to whether there might be essential regulatory interactions that prevail across diverse cellular contexts. To address this question, we have constructed a large-scale cardiac signaling network by integrating previous experimental results and developed a mathematical model using normalized ordinary differential equations. Specific cellular contexts were reflected to different kinetic parameters sampled from random distributions. Through extensive computer simulations with various parameter distributions, we revealed the five most essential context-independent regulatory interactions (between: (1) αAR and Gαq, (2) IP3 and calcium, (3) epac and CaMK, (4) JNK and NFAT, and (5) p38 and NFAT) for hypertrophy and apoptosis that were consistently found over all our perturbation analyses. These essential interactions are expected to be the most promising therapeutic targets across a broad spectrum of individual conditions of heart failure patients.