Yes, you were correct in using the s/n in the battery compartment. I am not sure what the number is that appears on the start-up screen of the V3, which is directly underneath the version, it maybe a line of software/version code, like html code - this is NOT the serial number of your unit.
However, if you register your unit online, use the serial number located on the sticker inside the battery compartment. This is the serial number for your unit, the s/n number inside the battery compartment should match the serial number on the actual warranty card. I hope this clears up any confusion.
HH - Andrea H.