[alpha]+[arrow keys] is rarely useful. It’s meant to scroll several lines at a time, typically when you’re programming.
[alpha]+[other buttons] is used for accessing variables. All those green letters above the main keys show what variable the calculator will display when you press it with [alpha] enabled. (Note: the white space, colon, question mark, and double quotes; along with the f1 through f5 buttons (at the very top) are not variables, they have different functions.
As for your solution: You may have accidentally turned on alpha-lock (this allows you to keep typing variables without needing to repeatedly press [alpha]). It can be easily fixed by pressing [alpha] again. If for some reason that doesn’t work, turn your calculator off and back on again.
You may want to familiarize yourself with the user-manual. ;)