Seagate Expansion 1TB
I bought a Seagate 1TB Expansion External Drive under a month ago. It was working fine until a few days ago it decided to stop working. The harddrive's light blinks when loading up and then stays on when it's finished. (This is normal) Windows beeps when it is plugged in recognising it. So the harddrive is picked up by windows somewhere. Under a minute, i havent timed it, it freezes my computer completely, except for my mouse. My computer does recognise it. And it shows itself in device manager as a USB Mass stoaage device now. Before it was Unrecognisable USB Plug.
Have you tried changing the USB cord on the HDD also a different USB port?
A good tool for diags is http://www.seagate.com/www/en-us/support/downloads/seatools
there is a tutorial that walks you through on the website and tells you what to expect.
the following link is an External Hard Drive Troubleshooter for Windows 7 and Vista 
finally go here to check on your drive's warranty status
If you bought the drive from certain vendors like costco you have 90 days to return the item
best of luck