Dear Bob,
Unfortunately, there is no "cooling off" law when you buy a car. Once you bought the car, it became yours. You cannot return it if you decide that you do not want it.
Also, because you bought the car from a private party, the Minnesota "Used Car Warranty Laws" do not apply. The Used Car Warranty Laws also do not apply if you bought the car "as is."
You may have heard of the "Lemon Law," which is Minnesota's Motor Vehicle Warranty Statute to protect you when you buy or lease a new vehicle that is still under the original manufacturer's warranty. Because you purchased the car from a private party, I assume the car is not new. If it is not new it is not covered by the "Lemon Law." However, if the used car is still under the original manufacturer's warranty, the Lemon law may apply. The law helps you enforce the manufacturer's written warranties. It generally does not allow you to return the car without going through a reporting process to the manufacturer, and letting the manufacturer attempt to fix the problems. If it cannot be fixed, it will be considered a "lemon" and a refund or replacement of the car may be allowed.
From the information you provided, it seems to me that you are probably stuck with the car that you purchased. For further information about Minnesota's car laws, please refer to Minnesota Statute Section 325F.665. You may also obtain information through the Minnesota Attorney General's Office at http://www.ag.state.mn.us/Consumer/Auto/Default.asp, by calling them at 1-800-657-3787, or writing them at 1400 Bremer Tower, 445 Minnesota Street, St. Paul, MN 55101.