I would write to the general manager of the hotel. You should be able to get the GM's name by calling either the hotel or the silver customer service line.

You should explain what happened during your stay, focusing on the inconvenience of a noisy A/C and the circumstance of your trip. I would also note that you felt the front desk did not have the right attitude regarding your problem upon check out.

You could ask for a partial refund or a credit of Marriott points to your account. They may be more willing to give you points since they can buy them at a discount. Personally, I would not request anything specific. Instead, I would let the GM or one of his supervisors suggest appropriate compensation. If I was unsatisfied with their offer, I would make a request for additional compensation.