Is there any screwer at bottom cover of the drive?
It could be hidden under ribbon parts of the bottom side.

The underside of the enclosure has four screws that look like tamperproof torx screws; however, I tried a set of tamperproof torx drivers at the local Sears, and none of them fits the screws.

Can you take a photo and post it here?

Here is a photo.  Screws look like tamperproof torx, but torx drivers don't fit it.  Thanks!
STA-0985.JPG

I think you need to look for exactly same screwer to fit exactly this model. Seagate tried to prevent opening their boxes this way =)

Thanks. I  was hoping that somebody knew a source for the tool to open it.  As you probably know, Seagate is no help.

Thanks.  That's just what I will do!

After visiting two repair shops, neither of which had the tool, I decided to do what I should have done when I first figured out that the screws were not standard torx -- drill them out!  Once I opened the enclosure, there were two T10 torx screws to remove the drive, and put it in a working enclosure.  The drive works fine in its new enclosure.

Thanks for feedback.

It seems those screws are a pentalobe 5-point star, whereas common torx is a 6-point star. Some of the newer Apple equipment like the iPhone series and MacBook Air series reportedly use some of these same tiny 5-point star screws because they are "tamper-resistant" due to the rarity of the bits. Sets of pentalobe screwdrivers and bits can be found from common online vendors. Beware the size you need. It appears the Seagate in question uses a TS-6 or TS-7 bit. Some European auto makers apparently use much larger sizes for their cars, so when you look online to buy some pentalobe bits or screwdrivers make sure you order the tiny ones for computer/electronics.

I think I'm going to resort to the "drill it out" option on my own Seagate ST 90000U2 because my TS-5 pentalobe bit it too small and I don't want to wait for an online purchase to arrive.