I'd be concerned how they were able to control the computer to begin with, the exe on the dropbox url is a second point of attack, the first point is that they were able to control it in the first place. I'd be looking to discover how the first point of attack happened, as clearly AVG did nothing to prevent that happening.
Boot in safe mode, bring up an MS Config window and see if there are suspicious processes loading during a typical Windows boot up. Malware/Viruses can hijack anti-virus apps, and i'd not be convinced AVG is protecting you, as clearly someone was able to hijack control of your computer the moment you were away. How that happened, would be priority number one were i in your shoes.
What browser are you using? Does it have any third party addons installed? And is your windows upto date?
EDIT: Reading that back again, this sounds like a browser hijack to me.