Start again.
Delete the existing desktop shortcut. (Right click on it and select 'Delete'). Access Hotmail/Outlook via your web browser. When you get to where you want to be, reduce the size of your browser window to less than full page (by clicking on the overlapping squares in the top right hand corner). You'll now be able to see some of your desktop behind the window. Drag-and-drop the favicon (immediately to the left of the URL in your browser's address bar) onto your desktop. You'll then have a new shortcut which, hopefully, will work for you. (If you need to rename the shortcut, you can do so via right-clicking and selecting 'Properties').