Due to the age and likely mileage of the vehicle you are probably out of luck as Minn. Stat. 325f.662 exempts cars sold for less than $3000 or with more than 75,000 miles from any warranty requirement, unless there were specific representations about the quality and condition of the vehicle, which could possibly be false advertising or a deceptive practice. However something else of concern is the fact that you bought this car from a dealer at his home rather than his lot. This is potentially a violation of his dealer license.
Nicholas is right about it being generally illegal for a car dealer to sell cars anywhere but at their car lot. That alone may give you some legal rights and some practical leverage to get the dealer to help you out. In some states, it is also illegal for a car dealer to sell a consumer a car that is dangerous to drive. In a used car sale, your legal rights are mostly determined by the paperwork that you sign. Look to see if anything was written down about any kind of warranty or guarantee or right to cancel the deal. But that’s not the end of it. There’s also a federal law that requires all car dealers to post on the window of all used cars they are selling a special “Buyer Guide” form (it’s often called a Used Car Window Sticker) that discloses whether or not a warranty comes with the car. Many small lot car dealers don’t comply with the law. If they don’t, then you may end up with a warranty after all and you may even have the right to cancel the sale. The back side of the form has to be completely filled out and many car lots, big and small, fail to do that too and that can also trigger your right to cancel the deal. You can see what the Buyer Guide form looks like on this web site page: http://ohiolemonlaw.com/used-car-lemon-law.html . You need to talk to a local Consumer Law attorney who deals with this kind of case (it's called "autofraud" or car sales fraud). Call your local attorney's Bar Association and ask for a referral to a Consumer Law attorney near you or you can go to this web site page for a Free Online 50 State National List of Consumer Law Lawyers (http://www.ohiolemonlaw.com/ocll-site/ocll-locate_local.shtml) and find one near you (lawyers don’t pay to get listed here and most of them are members of the only national association for Consumer Law lawyers, NACA.net). But act quickly because for every legal right you have, there is only a limited amount of time to actually file a lawsuit in court or your rights expire (it's called the statute of limitations), so don't waste your time getting to a Consumer Law attorney and finding out what your rights are. If this answer was helpful, please give me a thumbs up below.