First thing is to double check the power to the drive to make sure the power light is on, and it is spinning OK. Also remove and reinsert the USB connector lead at both ends.
Then when connected to your desktop, go into the BIOS in the Standard CMOS settings to see if the computer recognizes the hardware.
Then, go to Disk Management and see if Windows sees the removable HDD, in the lower graphical section.
It may be listed as DISK 1 or DISK 2, depending on what else you have connected.
If it is recognized in Disk Management, report what it says under the Disk Status column, and the Volume Status column. Also the color of the band above the Volume Status area.
that way someone will be able to get it going again.