I guess you were using the website. If you use a web browser accessing www.drivehq.com, it doesn't support drag and drop; but you can use Cut and Paste buttons in the tool to move files.
It is strongly recommended using DriveHQ FileManager 4.0 client software. It works just like Windows Explorer (My Computer), supports drag and drop; it also supports file sharing and folder synchronization, etc.
If you are using Mac or Linux, you can also use DriveHQ FTP service, which is fully integrated with DriveHQ online storage and sharing service. For more info about DriveHQ FTP, please visit:
http://www.drivehq.com/ftp/
FTP client software can be found in the software tab.