I don't know what might be causing this.
You are on Windows (looking at the screen shot)? Is it Windows XP or earlier?
Some keyboards have a regular enter key and a keypad enter key. Which one are you using? (The keypad enter key always acts as shift-enter, I believe).
This shouldn't matter, but I presume your caps lock and num lock are not turned on?
Your keyboard layout is just a regular US keyboard layout or a non-US layout (if so, which)?
No special key mapping or tracking software installed?
Keyboard itself is functioning OK (no strange/random shifted characters due to a malfunctioning shift key)?
I found another user with the same problem here (but no solution): http://forums.wolfram.com/student-support/topics/524139
lso, you don't have "sticky keys" turned on by accident?