Was Amazon the direct seller of Vegas Movie Studio or was the seller a 3rd party individual or company using the Amazon platform as a means to sell Vegas Movie Studio? If the former, you'd need to contact Amazon about the issue and then if necessary contact MAGIX at infoservice@magix.net about the serial number that's been sold.

If the latter, you'd need to contact the 3rd party seller to resolve the issue. A few years ago, there were unfortunately a number of reports on the forum of 3rd party sellers selling Vegas products (possibly secondhand) on Amazon's platform but with dodgy serial numbers that didn't work.