ONLY Revision B hardware is compatible with Windows 7. See this page on D-Link DUB-E100 Drivers.
You did not mention if this is a 32 bit or a 64 bit operating system. But to begin troubleshooting I would go to device manager and see what the driver is listed as if it is listed at all. If it is listed remove it and allow it to be re-detected.
If it is not listed in device manager it is probably not getting the proper voltage from the USB connection. Make sure it is not plugged into a USB hub and it is plugged directly into a USB 2.0 port.
The hardware is compatible and native to Windows 7 so once you complete one of the above steps the device should be accessible and ready to use. Let me know how it goes.