I had this issue on another machine and in the end it was the motherboard chipset drivers and not the OS or the drive.
I see you write you installed Windows 7 but no mention of motherboard chipset drivers. I can't find the model number to look up a driver for you.
I'd try the motherboard drivers first and as always do not use Windows to find them.
I have a 320GB WD Passport Elite external USB drive. Previous to that drive I had a 160GB model which always worked fine. This drive itself initially worked okay. Recently it has been locking up while writing to the drive. I can be using backup software or merely copying things from Windows Explorer. It doesn't matter if it is a large or small file, it just randomly stops copying within a few seconds after the copying starts. I still see the copy dialog open indefintely, but the LED lights on the drive stop flashing and remain solid (it sounds like the drive is spinning continously but the drive head is not moving). Usually at this point, I cannot even cancel the copy command, and if I try going into "My Computer" explorer locks up until I pull the USB cable out.
Reading from the drive is fine, it is only the write commands.
The drive works fine on my laptop and at work, and only doesn't work on my desktop at home. I also tried another 250GB WD drive and it has a similar write failure.
I also tried using a USB Y connector to utilize two USB ports (whether on the front or back ports) and still get failures.
Finally, this was a problem under Vista 32bit. I just formatted this computer (Dell XPS 400) and installed Windows 7 Home Premium and still has the same issue.