Legal Question in Landlord & Tenant Law in California

The landlord and the tenant both have the responsibility of maintaining the premises in a habitable condition. If you did not notify the landlord at the time when you failed to pay rent of the roach problem as the reason for withholding the rent, then the landlord cannot know about it. Since you continued to live at the location, apparently the roaches didn't make it completely uninhabitable and likely it will be found that you were required to have paid at least a reasonable portion of the rent.