I'm wondering how to read the Serial # to determine the year of the machine.

Very few serial numbers give indication of year of manufacture
a year of manufacture will show when a serial number began but will not tell how many years variations of that serial number ran for
for example in 1990 a serial number 0010101 was started for the first item produced but after 10 years the serial number will be 00101999 so 001011596 will not show a year of manufacture just that it was produced between 1990 and 2000
to add more confusion
in your particular question example a model 7800576 could have been produced in 3 different countries and the serial number will be from any one of those countries as each set of serial numbers will denote which country it was made in
may be it you contacted the manufacturer technical division, they may be able to provide a matrix that will answer your question better