This is a letter where I am complain for a complaining about bad service

Dear Sirs COSTA HOTEL or Madam,
I am writing this letter to express my displeasure at the poor service I received yesterday, on July 1, 2014 in at the COSTA HOTEL., according to ABC-12345 reservation number. For me, this would be one night of comfort in a five star hotel, listed as one of the best hotels in the city. However, this was one of the worst experiences I've had in hotels in this category.
When I entered to my room I realized that the air conditioning does did not work and the room was dirty. I spoke with the staff to ask to be moved from room to a different room and they told me they had no rooms available and that the maintenance staff would solve my the problem. Finally, they were able to repair the air conditioner at 1 am and to clean my room.  They did not caring care that I had an international flight the next day and I needed to be at the airport at 4 am. and I couldn't sleep or rest as was my goal.
I would like a full refund of the cost of the room as soon as possible, otherwise, I'll talk to my lawyers and I'll complain about you publicly. I look forward to your prompt reply or my lawyer's will be called.

Please, help me to learn English :)

For the sentences highlighted in Red and Pink, I have written replacement sentences below.  I hope this is helpful.

The hotel was listed as one of the best hotels in the city, however, this was one of the worst experiences I've had at a 5 star hotel.

As a result I couldn't sleep or rest before my flight.

This is a letter where I am complained about for a bad service.

July 2, 2014

Dear Sirs: COSTA HOTEL

I am writing this letter to express my displeasure at the poor service I received yesterday, July 1, 2014 in at the COSTA HOTEL, according to ABC-12345 reservation number. For me, I was hoping I would experience a this would be one night of comfort in a five star hotel, listed with a reputation as one of the best hotels in the city. However, this my stay was one of the worst experiences I've had in a premium hotel hotels in this category.

When I entered to my room, I realized that the air conditioning does did not work and the room was dirty. I spoke with the staff and asked to ask to be moved from to another room. and they They told me they had no rooms available and that the maintenance staff would fix the room solve my problem.

Finally, They were eventually able to repair the air conditioner at 1 am and to and clean my room, but not until 1 AM! not caring that [You don't really know if they cared or not. I recommend you just state that you had to get up early.]  However I had an international flight the next day, and I needed to be at the airport at 4 am, but and I couldn't sleep due to all the problems. or rest as was my goal.

I would like a full prompt refund of the entire cost of the room as soon as possible, otherwise, I'll talk to my lawyers and I'll complain about you publicly. I look forward to your prompt reply. or my lawyer's called. [No need to mention your lawyers again. You've already said you will call them.]


Please, help me to learn improve my English :)

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Nicely done!

In the second paragraph, you jumped between present and past tenses. Since you were talking about the past, you should stay in past tense all the way through the paragraph. A number of my edits there corrected for the past tense. Some of the other edits just changed the text to be more to my liking.

I am sorry to read about your stay. What a nightmare!!