offspon.exe is the process that displays the rotating advertisements in Microsoft Office Starter Edition. It is a legitimate program, but because its sole purpose is to display advertisements, AVG may detect it as adware, and display a warning. Even though it is indeed a form of adware, it is 100% non-malicious and harmless, so it is safe to tell AVG to ignore it.
So blocking this one .exe should not have blocked your access to the internet.
Go into Security Center, select Firewall, and then select 'Internet Connections for Programs'. Look for anything that says 'Block'.