To take a screenshot in windows without copying and pasting, open the start menu and navigate to All Programs > Accessories > Snipping Tool.
You should have a new window that looks something like this.
Click New and draw a rectangle around the desired area.
The window will then resize and look something like this.
Click Save and select the location to save the screenshot.
Then from within Zendesk, just attach the image (png) file to your ticket or as an email attachment if you are emailing tickets in.