There is only one good reason an LCD will be black - the LCD's fluorescent backlight is not turning on.

Things that might cause this are limited, including a bad backlight or no power being delivered to/from the inverter (located beneath the LCD). Even if the LCD screen itself was bad or the video data cable was messed up, the screen should at least turn solid white when the laptop is turned on and shows its first image (the Apple logo).

The most likely cause for inverter problems is you've left a cable loose. I know you say you've double checked, but its too much of a coincidence to ignore. I'd triple check and make sure the inverter is plugged in snugly and that the connection on the board itself is also snug. There's also the possibility of a bad backlight on your LCD. Maybe the replacement you received is defective.

If it still doesn't work, I would try temporarily hooking up your old LCD to cross check and see if you get a picture. If you don't -- then you know something has changed. Maybe the inverter was damaged during handling or this is part of another problem where your computer isn't booting up far enough to show a picture for some reason. (the Apple chime is a good indicator it probably works well enough to show a picture though).