I recognize that Outlook under Windows isn't a hot growth area for email clients... but this trick has worked for me for years:
Create a shortcut to Outlook on your desktop, and set the shortcut target (right-click, Properties, Shortcut tab) to
"C:\Program Files (x86)\Microsoft Office\Office14\OUTLOOK.EXE" /c ipm.note
Change the path to wherever your Outlook really lives.
Then, also on the Shortcut tab, set a shortcut key. I use Ctrl+Shift+Alt+M, but anything that doesn't conflict with something else will work.
I also name the shortcut (on the General tab) as "New Mail message"
Once that's all done, and you log out and back in again, pressing your shortcut key will bring up a new mail message, even if you don't already have Outlook running. It will be (much) faster if Outlook is up and running in the background.
This works regardless of what program is in the foreground - as long as the window that has focus doesn't have a shortcut key that matches the one you set, you can open a new mail message from anywhere.
The same trick can work for other Outlook data types - see Outlook's help on command line parameters to figure out what the shortcut target should be.