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Yes, the dealer should be responsible.
You will have a variety of damages possible and you want a lawyer to help you with this, you can recover your attorney's fees, because on the possible damages is to get the money for the car that you thought you were buying which is a substantial chunk of money. It will be hard to "prove up" the damages and so a lawyer will need to help with that. You can also potentially recover other damages including, possibly, treble damages due to the misconduct and false advertising.
Your lawsuit will be based on breach of contract, false advertising, and deceptive trade practices.
If your question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a Positive Rating so I receive credit for my work.
Of course, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered. In addition, once you issue your Positive Rating the question will lock open and no longer time out so you can come back to it anytime in the future if you think of any follow ups.