Here is a solution I discovered.
While I encountered this post two years later, I found the information quite useful.
Not only did I use the Maxtor OneTouch III to backup my hard drive, but I too used it to store large Family Home Videos and Music files. After having the drive for two years, the drive would do nothing but "Click". For those wondering if this is the same thing their drive is doing, the "click" occurs every second repeatedly until you turn the power off.
I tried unplugging the device for awhile. I then swapped the USB cable thinking it might have been a bad cable. I tried the various tricks with Device Manager to get the USB drive to be recognized, etc, etc. I tried several computers with varoius operating systems to no avail.
After contacting Maxtor/Seagate support, I discovered they consider this a "Failure" and even if you get them to honor or even extend the warranty, they will only exchange your drive for a new one. Of course, the data and family video files are worth more than a "new" drive so I thought about purchasing a known good drive and swapping out the hard drive to see if I could get it to be recognized. Ultimately, I decided go ahead and purchase a new back-up device, however this time I bought 1.5TB for $90 (Not bad!). I then decided to go ahead and VOID any warranty by cracking the case of the Maxtor OneTouch. The case has two (2) screws on the back (One is under the warranty seal sticker). I then used a small flat head screw driver to help pry the case away from the metal chassis (the side panels have "slider tabs"). I then removed the chassis screws and discovered the Maxtor OneTouch is nothing more than a 500GB Barracuda IDE (80 pin) hard drive. I then took that drive and installed it in my other computer, and it started spinning immediately. PROBLEM SOLVED. And I didn't have to pay someone $1500 to recover my data! No more clicking. While not conclusive, this experience supports other posts claiming the problem is in the Maxtor casing design.
The drive continues to work fine however, I now have my files backed-up in multiple locations. I am not yet ready to allow some offsite/online backup service take all of my personal data.
UnchainedSmoker