how do you put "My Computer" on the desktop when there is no pull down menu from the one in the start menu?

Do you mean that my computer doesn't appear in the start menu?
If so right click on the start button > properties > customise > advanced then scroll down to my computer and tick the display as link button.

oh yes, it shows in the start menu, I just want to have a shortcut on the desktop, too.

Right click the my computer button and put a tick against the show on desktop tab. Or doesn't yours let you right click?