Welcome to Android Central! Just to be sure -- the phone is still able to connect to the web via mobile data? When you connect the phone to the computer via USB, does the computer register that something has been connected?
What version of Windows is your laptop running? When you used to do it before, was that a while ago (like on Windows 7), or not too long ago? The S3 is a really old phone, so I'd wonder if something has become incompatible with more recent Windows updates.