It could be a bad power source (power cable). You may want to try plugging into a different outlet, or directly into an outlet if you happen to be using a power strip and/or surge protector. If that fixes the problem, you are in luck.
More than likely, the controller on your hard drive is bad. Your hard drive works fine, you can void the warranty by smashing open the plastic or carefully unscrewing it, taking out the standard 3.5" drive inside, plugging the drive into any desktop (work, home, a friend's machine) and copying the data to a new hard drive. Alternatively, brick and mortar stores like Fry's and Micro Center sell "hard drive enclosures" and you can buy them from newegg, amazon, or ebay. These enclosures have hard drive controllers.
Seagate will recommend you send them your drive so they can fix any hardware problems for you, and then they will tell you that they *must* reformat the hard drive to *fix* it, but for a fee they can recover your data. The fee will be more than the cost of a new hard drive, and they are planning on either (a) your employer will reimburse all of the money because it is your employer's data, or (b) you will pay through the nose to get that data back because it has your life's work or unforgetable, irreplacable data like your escrow paperwork, photos of late relatives, etc.
A new enclosure cost less than 1/10 of the recovery fee. Also, you get a fully working drive with all of your old data the second you buy the enclosure, no shipping and handling. The enclosure is literally 8 tiny cross-tip (phillips) screws; 4 on the inside, 4 on the outside. The 4 on the outside are as easy to remove as a bad light bulb, and the 4 screws inside are as easy to remove as the screw on the hinge of your reading glasses (about the same size, too). Opening the enclosure without breaking any plastic bits PROBABLY has a video on youtube, but I would just smash it open since you can't reuse the case anyway, the case has a bad controller. When you open the enclosure, you will see there is a mother board smaller than a credit card with the blinking LED's on it, and it takes the electricity from your USB as input, and turn that into SATA for an output. The actual 3.5" hard drive has a SATA port that can connect directly to any desktop computer or any other hard drive enclosure (provided the "other" enclosure was not made 6 years ago).
