There's many things you can try. 1. Force it into restore mode, and then restore through iTunes. 2. Force it info DFU mode and restore it in DFU mode through iTunes. (1) Make sure your iTunes is up to date. (1) Try another cable or USB port. (1) Disconnect the battery for a good minute or two, reconnect it and try again. If none of that works it's probably cooked.
You've either damaged the connectors (physically or with ESD) or they aren't connected properly. If you're 110% confident they're connected properly, a new screen would probably fix it.
