You brought it from a business but they reckon its a private sale. Who did you make the cheque out to and is there a letter head on the receipt? I don't think they can get away with that private sale disclaimer at all.
As others have said,its time to ring the ACCC. I would also keep the people you brought the motor off informed of everything you're about to do on the matter. Don't be bullied into not posting the problem on here especially seeing you haven't named names YET!
Send the business a copy of this thread.