When broken AC can support a claim
You may be able to, but it depends on the situation. A claim is stronger when the landlord provided AC and refused to maintain it, when a local law required cooling, or when the broken AC ties to a real habitability or safety problem — not simply because a unit lacks AC.
Because state law does not require air conditioning, the key question is whether the landlord had a duty here. That usually comes from the lease, a local ordinance, a fair-housing accommodation, or a related habitability issue like mold from a leaking unit.
Whether you have a strong claim depends on those facts and how the situation affected you and your household. No attorney can promise an outcome without reviewing the details, and you should be cautious of anyone who does. A free, confidential review is the best way to find out where you stand.
This is general information about California tenant rights, not legal advice. Every situation is different.