What rights do I have when it comes to asking my landlord to fix the air conditioner?

An air conditioner in your state is critical; the failure to provide one in or for the summer may violate the implied warranty of habitability, or the obligation imposed on landlords by the law that rental units be habitable and fit for their intended purpsoe (i.e. residency). If you haven't already, send landlord a written notice that the A/C is not working and request its repair; also, keep a daily temperature log as evidence of the conditions, should you need it later in court. If the landlord does not repair the A/C within a reasonable time (say, around 2 weeks or so) of the written notice, to force the issue, you may need to withhold rent to force the landlord to make the repairs. The landlord might choose to try to evict you for nonpayment, rather than repair; if so, you can raise the failure to provide a working A/C as a defense in court to eviction and legal justification for not paying rent. The judge, if he agrees about the severity of the situation, may order the landlord to repair the A/C and/or may give you a rent abatement (credit) for the time you have been living without A/C. However, keep the withhold rent money available, in case the judge disagrees and requires you to pay it to the landlord to avoid eviction; or wants you to deposit it with the court, to be held in trust pending full resolution of the matter.