What does a goodman air conditioner serial number 9604109804 tell you?

Probably made in 1996. cant tell much more without the companys unique nomenclature

The serial number does indicate that the unit is a 1996 model, and it was manufactured in April of 1996 (the second 2 digits are the month, first 2 are the year), however that doesn't help much. You can find out more information if you know the original owner's name. Go to www.goodmanmfg.com, click WARRANTY in the list on the left, then click WARRANTY LOOK UP. It will ask for the first name and last name of the owner, but this must be the original owner for whom the system was registered. It will ask for the serial number or zip code. The result will be the model number, type of system, warranty type and length, date it was installed, and the contractor who installed (or at least the one whom it was registered under).