You are in deep, deep problem now.
I am saying this as I went through a similar experience several years back. I had found a car to my liking at a car rental shop in Aziziyah. By the time we had finalized the deal, it was around 9:30 pm. I made the mistake of paying him the money and took a receipt from this rent-a-car company. The company was being run by a Sudanese national. The company has now closed down.
The next morning when I went to get my car transferred, the Sudani owner put it off to "bukra Inshallah." The "bukra and Insha Allah" continued for four months.
But in those days, a policeman at the Central Police Station did try to help me. The policeman called him several times over several weeks and he always gave him some story and a promise to return my money within a week. That never happened. The policeman then gave up and asked me to go to the court.
During all this period, the Sudani kept on taunting me telling me that he had been in Qatar for over three decades and knew all the rules of the game.. He claimed with pride that I could do him no harm.
Why was he not transferring car? The workers in his office told me the Sudani could not transfer the car as he had bought it against a bank loan and he did not have the money to pay the loan back. As such he does not have the original documents in hand.
I went over to the Sharia court in Dafna with the intention to lodge a case against this crook. Luckily (very luckily) I met there a person from Eriteria who advised me to avoid lodging a case as it would take many months (around 10-12 months) for the case to get decided. He told me that on all dates set by the court for the hearing, I must be present whether the other side is present or not. The Sudani crook knew about this and what this meant for a working man who needs to attend office daily,
I did not file a case. I took the help of some very good Sudanese friends who intervened and helped me get my money back in three installments They made him give me three post-dated cheques which I happily accepted them. This is because I knew what would take place in the future.
As anticipated, the first cheque bounced. I took a letter from his bank and was to go over to the police the next morning.. That did not take place. The Sudani paid that evening.
I am writing my experience in such detail as I wish all QLers to know and be wary of such crooks operating in Qatar. All is not holy here.
As for your matter, it is for you to find a way out. If you go over to the Shariya Court, you may find a lawyer or two hanging around there but then lawyers are lawyers and they are the same the whole world over. They will promise you they can getting the verdict within "two months". Don't fall for their promises.
Getting your money or car will take time. I guess, your current situation demands you file a case against the company which is trying to cheat you out. It may send a message to them and give them something to worry about.