IANAL
From https://www.leg.state.nv.us/NRS/NRS-118A.html#NRS118ASec315 in NRS 118A.290 Habitability of dwelling unit.
The landlord shall at all times during the tenancy maintain the dwelling unit in a habitable condition. A dwelling unit is not habitable if it violates provisions of housing or health codes concerning the health, safety, sanitation or fitness for habitation of the dwelling unit or if it substantially lacks:
(h) Floors, walls, ceilings, stairways and railings maintained in good repair. (i) Ventilating, air-conditioning and other facilities and appliances, including elevators, maintained in good repair if supplied or required to be supplied by the landlord.
Summary: The landlord has an obligation to keep the AC in working in order and the dwelling unit is not habitable if the AC is not kept in working order.
From REMEDIES - NRS 118A.355 Failure of landlord to maintain dwelling unit in habitable condition.
NRS 118A.355 Failure of landlord to maintain dwelling unit in habitable condition.
1. Except as otherwise provided in this chapter, if a landlord fails to maintain a dwelling unit in a habitable condition as required by this chapter, the tenant shall deliver a written notice to the landlord specifying each failure by the landlord to maintain the dwelling unit in a habitable condition and requesting that the landlord remedy the failures. If a failure is remediable and the landlord adequately remedies the failure or uses his or her best efforts to remedy the failure within 14 days after receipt of the notice, the tenant may not proceed under this section. If the landlord fails to remedy a material failure to maintain the dwelling unit in a habitable condition or to make a reasonable effort to do so within the prescribed time, the tenant may: (a) Terminate the rental agreement immediately. (b) Recover actual damages. (c) Apply to the court for such relief as the court deems proper under the circumstances. (d) Withhold any rent that becomes due without incurring late fees, charges for notice or any other charge or fee authorized by this chapter or the rental agreement until the landlord has remedied, or has attempted in good faith to remedy, the failure. 2. The tenant may not proceed under this section: (a) For a condition caused by the tenant’s own deliberate or negligent act or omission or that of a member of his or her household or other person on the premises with his or her consent; or (b) If the landlord’s inability to adequately remedy the failure or use his or her best efforts to remedy the failure within 14 days is due to the tenant’s refusal to allow lawful access to the dwelling unit as required by the rental agreement or this chapter. 3. If the rental agreement is terminated, the landlord shall return all prepaid rent and security recoverable by the tenant under this chapter. 4. A tenant may not proceed under this section unless the tenant has given notice as required by subsection 1, except that the tenant may, without giving that notice: (a) Recover damages under paragraph (b) of subsection 1 if the landlord: (1) Admits to the court that the landlord had knowledge of the condition constituting the failure to maintain the dwelling in a habitable condition; or (2) Has received written notice of that condition from a governmental agency authorized to inspect for violations of building, housing or health codes. (b) Withhold rent under paragraph (d) of subsection 1 if the landlord: (1) Has received written notice of the condition constituting the failure to maintain the dwelling in a habitable condition from a governmental agency authorized to inspect for violations of building, housing or health codes; and (2) Fails to remedy or attempt in good faith to remedy the failure within the time prescribed in the written notice of that condition from the governmental agency. 5. Justice courts shall establish by local rule a mechanism by which tenants may deposit rent withheld under paragraph (d) of subsection 1 into an escrow account maintained or approved by the court. A tenant does not have a defense to an eviction under paragraph (d) of subsection 1 unless the tenant has deposited the withheld rent into an escrow account pursuant to this subsection.
Summary: If you gave written notice more than 14 days ago, you are within your rights to withhold rent (section 1 d), but depending on your local jurisdiction you may be required to deposit it into an escrow account (section 5). If you have not done that properly, then I recommend that you pay the rent now, provide the notice properly, and then proceed with the option(s) of your choice. Option d does not require you to go to court but will require you to pay the withheld rent once the defect is fixed. Option b may allow you to simply provide the list of damages but may require you to go to court to have them paid if the landlord refuses to pay them (this of course increases the damages, since you’d be paying court fees, taking time off from work, and so on). You could take both routes of course.