I don't think you can view the phone on the computer unless you input the password? Which would be difficult as the digitiser is probably faulty too.
If you can't access anything on the computer I would do the following:
Use a S3 to hdmi to plug into a tv (amazon or ebay) and see if you get anything, if you do, and if you're lucky, the touch screen might work, so you can see on the tv screen and guess approximately where ro touch the screen.
NOTE: charger must be plugged into the small box also for it to work
once unlocked, quickly plug into the computer, swiping the screen every few seconds to prevent it from locking.
im sure it wont do anything until the code is in, otherwise, any monkey could plug your phone in and take what they want.
hope this helps.