It might be that the serial number is under the machine head, or in an otherwise inaccessible location which would require the machine removed from the table to find. That's a 2 person job.
I'm not sure why you need the serial number at this point. I recently bought a used APQS millennium, and spoke with the company directly prior to purchase-all I needed was the sellers name and they looked her up in their records and gave me all the information on the machine they had.