Mainly, you have to give them a reasonable number of attempts to fix OR a reasonable time to fix. If they have not fixed or cannot fix within that...

Can we get our money back?

It would be nice to know about the state of the tranny prior to the sale and what kind of warranty, if any, you received. I am completely against...

Breach of contract

You put money down on a car. You did not get that car. Do NOT do business with these folks again. Get your money back and move on, IF you are lucky...

Do I need to take this to court

So, you paid the car, did not get title and then wrecked it? Maybe and this statement is rare, maybe the court is the best way to sort this...

Is there anything I can do?

Your opening line, that you were completely lied to, is your starting point. The quicker you jump on it, the more rights you will have. Seems like...

Do I have a case?

Have it looked at by an expert and contact a consumer protection atty right away. Find someone qualified here: http://www.naca.net

Can I return a used car that I just bought?

Like Ron Burdge says, maybe, maybe not. If there was fraud involved or undisclosed problems that are material, most states will allow you to...

Do they have to reimburse my money?

Generally, no. If there was fraud involved, that's a different story...

Is there anything I can do about the car I just bought?

If the issues are in fact "major" as you've described or "material" a dealer would have to disclose, in most states. An example would be a severe...

If i have already paid for an item and i find out that it has been sold to another one though it was in poor condition

Very unclear. That said, some items, like, let's say, the statue of liberty, as singular and have great value. In those instances, you can arguably...