Depending on what data you're after, (pictures, videos, etc) then just plug it into your PC via the USB port, unlock the phone, and you can browse the storage directory structure via Windows Explorer, and copy anything that's there.

If it's stuff like call logs, contacts, and text messages, you might be SOL, but I'm not 100% sure. I've never had to recover that kind of data.

Unfortunately the screen is black and I need to authorize any connection. I'm gonna play with it some more when I get home.

You could use a service like TeamViewer (there's a mobile app that you can install on your phone, then you connect from TeamViewer on your PC) to be able to see what's on the screen ALL the time, if you can manage to get enough screentime to get that running.