I have never had a Seagate external. Western Digital, Iomega, Toshiba, never a Seagate.
Do you have access to another computer (maybe even a friend's that you could use for five minutes) for a test?
I have been thinking about your original post--I was not beating on all cylinders Saturday night when I wrote my response--something about a restaurant I dislike getting its revenge on me for dining there.
I have had Mint on several computers and have not yet experienced a problem mounting an external drive or other mass storage device (MP3 player, SD card, etc.). I plug it in, the icon appears in the file manager/desktop, I click on it, and it mounts.
I agree with you that something else might be going on here.
This article suggests some troubleshooting steps to help you get started: http://www.ehow.com/facts_7525769_pr...hdd-linux.html