Unfortunatley, the short answer is: no. Used car purchases are "as is". If you can prove the seller made some express promise about the condition of the car, which was false, and you can prove the seller acted fraudulently, it may be possible to rescind the agreement.. it is very difficult to undo a sale in your circumstances.
I think Mr. Spitters pretty much has a handle on this. I should add if there was some clear lie in an advertisement OR if you find that this seller is a "dealer" (selling 5+ cars a year) but not licensed to do so, then you may have grounds to undo the deal. Good luck with it.