Recommendation models utilizing unique identities (IDs) to represent distinct users and items have dominated the recommender systems literature for over a decade. Since multi-modal content of items (e.g., texts and images) and knowledge graphs (KGs) may reflect the interaction-related users' preferences and items' characteristics, they have been utilized as useful side information to further improve the recommendation quality. However, the success of such methods often limits to either warm-start or strict cold-start item recommendation in which some items neither appear in the training data nor have any interactions in the test stage: (1) Some fail to learn the embedding of a strict cold-start item since side information is only utilized to enhance the warm-start ID representations; (2) The others deteriorate the performance of warm-start recommendation since unrelated multi-modal content or entities in KGs may blur the final representations. In this paper, we propose a unified framework incorporating multi-modal content of items and KGs to effectively solve both strict cold-start and warm-start recommendation termed Firzen, which extracts the user-item collaborative information over frozen heterogeneous graph (collaborative knowledge graph), and exploits the item-item semantic structures and user-user behavioral association over frozen homogeneous graphs (item-item relation graph and user-user co-occurrence graph). Furthermore, we build four unified strict cold-start evaluation benchmarks based on publicly available Amazon datasets and a real-world industrial dataset from Weixin Channels via rearranging the interaction data and constructing KGs. Extensive empirical results demonstrate that our model yields significant improvements for strict cold-start recommendation and outperforms or matches the state-of-the-art performance in the warm-start scenario.