Why doesnt my external harddrive show up in my computer?

Then there are only 2 possibilities - either the enclosure does not play or there is a driver problem. As far as jumpers are concerned, I have no experience. Maybe you should try the different settings.

You would have to check on the Seagate site.

And have a look here:

http://pcsupport.about.com/od/fixtheproblem/ht/update-drivers-windows-7.htm

Nah, some disks do click at times. That is not necessarily a sign of a problem. But if that disk was never clicking before, then it may be a new problem.

The driver you are looking for could be for the HDD or the enclosure.

What is so important about that disk. Do you have data on it? Else I would just buy a modern Sata HDD. They are relatively cheap these days.

Consistent clicking would be a warning to me (not an odd intermittent click). If it is visible in "Device Manager" (not disk management) under Disk Drives you could try right click and select update device driver.
Also, if you have valuable data on the drive you could try a linux distro boot CD like "Puppy linux" and see if that recognizes the drive.