Writ to the landlord advising that if the dishwasher is not repaired very soon (provide a specific date) that you will retain a repairman and deduct the cost from next month's rent. Be sure to include a copy of the receipt with your rent payment.
Mr. Spitters is correct: you have a repair and deduct situaion. However, there is a specific code section that allows you to repair and deduct. It imposes some conditions and limitations, so be sure to talk to an attorney about this before trying to the problem.