Method 1 : Shortcut key or keyboard remapping
The fact is that this Media Direct Button just emulates a keyboard key. This means that you can use it as the key for any shortcut. Just right click any shortcut on the desktop, select Properties, click inside "Shortcut key", press the Media Direct key, then OK. This assumes that the program Dell Quick Set is not launched to confuse the issue.
Something else you can do with the Media Direct Button map it to any other key, by simply using keyboard mapping techniques.
All you need to do is download a program such as Keytweak, assign a hotkey to any shortcut on the desktop, and using Keytweak (or any other keyboard mapping program) to map the Media Direct button to this hotkey. From now on, pressing the Media Direct Button will launch the shortcut.
More detail is available in How do I ... remap my keyboard with KeyTweak?.
More complicated mappings of the Media Direct Button also require Microsoft Intellitype Keyboard Software. See the article
How to Customize Dell Media Direct Button to Hibernate,
for an example that sets the Media Direct button to hibernate the machine.
Method 2 : Replace MDdirct.exe
One more method for customizing the Dell Media Direct button uses the fact that all it does is launch the program
So all you have to do is replace it with another program or a compiled script (saving the existing file, just in case).
See the article Change the Dell Media Direct button for an example, where MDdirct.exe is replaced by Media Center.
This also requires the program Dell Quick Set (by default a Dell-installed startup program).