Didn't work. :( My old screen had died after I dropped the phone a few too many times (wouldn't display anything at all), so I bought a replacement from this site. Opened the phone, disconnected the battery, removed the old display assembly and plugged in the new one. Then plugged the battery back in and tried turning the phone on to see if the new display works and that it's not some problem with the phone itself - sure enough, got the "low battery" icon on the screen.
Unplugged the battery again and disconnected the new display as I still had to transfer the home button. After doing that, plugged the display back in, screwed the connector cover back on, plugged the battery in, and tested again - this time, nothing at all. Tried a few times to take it apart and put it back together, but to no avail. My only guess is that I could've damaged the cables when putting the connector cover back on. Not really willing to try buying a new display (and risk the same thing happening again) to test that theory, though.