It's not Snagit, but it's free.
These directions are specific to a Toshiba Laptop, where you must use the FN key for functions, but will work for other computers with a few alterations.
To save a screenshot as a png file, hold down the Windows key and press the FN key and PrtScn (Print Screen) button on your keyboard.
Now press the Win + E keyboard combination to open Explorer. In your Pictures library, you will find a newly created Screenshots folder which contains the screenshots you have taken, listed in chronological order.
You can still copy the screenshots to your clipboard, using FN+PrtSc, and Alt-FN-PrtSc captures just the active window to your clipboard.