I'm assuming you've waited for a while - sometimes they won't respond for a 30-60seconds or so after booting. If so, the digitizer is not working on the display. It could be a faulty display, but often it's just that it got disconnected. Follow these instructions steps 1-15. Notice the last thing you disconnected was the digitizer. Check the cables and connectors for dirt or pieces of glass or similar that could sit inside and keep the connector from fully seating - clean it out with air and/or alcohol swabs. Then click the cables back on the connectors in the reverse order of steps 13-15. You can now turn the phone back on and see if it's working. If it is working, make sure you have some not-conductive spacer on the back of the connector before you reassemble (see the foam in the pictures above - that puts pressure on the cable to keep it from popping off, and replacement screens often don't have it).
If it still isn't working you have either a faulty screen or a more serious problem on the logic board.