It's much more likely to be an unintentional assignment of a key macro (shortcut) to that key. Check in System Preferences > Keyboard > Shortcuts, where you can look through the various assignments, or just click the Restore Defaults button. If you have a keyboard macro program installed, try disabling it.
It might also be a flakey keyboard: Turn on the keyboard viewer by enabling System Preferences > Keyboard > "Show keyboard viewers in menu bar", then select "Show keyboard viewer" in that new menu. Now you should see immediately when that 'a' key is pressed, shifted or not.
Another thing to try is an external keyboard if you have one.