I would guess that either the new screen is bad or you didn't plug it in tight enough... Maybe do restore if you can to see if it's still in the land of the living... http://ipod.about.com/od/iphonetroubleshooting/f/Iphone-Stuck-At-Apple-Logo.htm
When you say "screen" did you mean the glass, (digitizer) or the LCD? Or both? I would go back if the restore does not work and try the old screen and see if it kicks back on then I would get another, since a lot of the cheap screens you get off the net are junk... I've had my share of bad ones myself...