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In order to have a legally enforcible contract, the Law of Contracts states, among other things, that there must be an offer and acceptance and it must be supported by consideration. If those requirements are met, then the parties have a valid, enforcible contract.
In your situation, here is what I see -
The dealer was offering the car for sale
You accepted the offer by signing the Agreement of Sale
The Consideration -
The dealer promised to have a safety inspection performed on the car on Monday
You promised to pay $2,000 down and obtain your own financing.
A promise in exchange for a promise is valid consideration and enough to support a contract. Therefore, there is a legally enforcible contract between you and the dealer. However, not only would it be poor public relations for the dealer to try and enforce the contract, but it would cost the dealer more in legal fees in trying to enforce the contract by filing a lawsuit against you for Specific Performance.
You could probably successfully get out of the contract by speaking to the dealer, telling him that you did not get the funds which would have allowed you to buy the car, and that you were unable to get the necessary financing. If the dealer again extends the offer to get you financing, tell him that you are not prepared to pay an exorbitant amount of interests that is usually offered with dealer financing. Lastly, although the points you raised are not legally valid to relieve you of the obligation to perform your responsibilities under the contract, you could still try to argue these points with the dealer.
I wish I could give you the Answer you were hoping for, and it would have given me great pleasure to do so, but I have an ethical obligation to give you only correct Answers, so I am respectfully XXXXX XXXXX you not hold the law applicable to your situation against me.
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