Rapid progress in generative AI has given rise to Compound AI systems - pipelines comprised of multiple large language models (LLM), software tools and database systems. Compound AI systems are constructed on a layered traditional software stack running on a distributed hardware infrastructure. Many of the diverse software components are vulnerable to traditional security flaws documented in the Common Vulnerabilities and Exposures (CVE) database, while the underlying distributed hardware infrastructure remains exposed to timing attacks, bit-flip faults, and power-based side channels. Today, research targets LLM-specific risks like model extraction, training data leakage, and unsafe generation -- overlooking the impact of traditional system vulnerabilities. This work investigates how traditional software and hardware vulnerabilities can complement LLM-specific algorithmic attacks to compromise the integrity of a compound AI pipeline. We demonstrate two novel attacks that combine system-level vulnerabilities with algorithmic weaknesses: (1) Exploiting a software code injection flaw along with a guardrail Rowhammer attack to inject an unaltered jailbreak prompt into an LLM, resulting in an AI safety violation, and (2) Manipulating a knowledge database to redirect an LLM agent to transmit sensitive user data to a malicious application, thus breaching confidentiality. These attacks highlight the need to address traditional vulnerabilities; we systematize the attack primitives and analyze their composition by grouping vulnerabilities by their objective and mapping them to distinct stages of an attack lifecycle. This approach enables a rigorous red-teaming exercise and lays the groundwork for future defense strategies.