Keep in mind that my reply is coming from the point of view of a dealer.
The dealer screwed up and should just eat it, but they probably won't.
Your main problem currently is getting them to sign over the title. They probably will not do that because in their mind, the unit is not fully paid for. For this reason, and assuming you cannot come to alternate terms with the selling dealer, you will probably need an attorney. You could also consider speaking with the Attorney General in the state the transaction occurred, and also contacting the Secretary of State's office in the transaction state as well.
For a purchase contract to be binding, you need three things: OFFER, ACCEPTANCE AND CONSIDERATION. Seller OFFERS to sell you a vehicle at a certain price. You ACCEPT it. You exchange CONSIDERATION by paying for it.
Where you have a sticky situation is if, as you say, the selling dealer denied acceptance of funds from the finance company/bank. This could be construed as denial of CONSIDERATION, and then you do not have a binding contract.
In any case, if you cannot reach an agreement with the seller, get a lawyer. You're going to need it.