Replacement LCD backlight on no image

Your best bet here is to double-check the display's ZIF connectors. It is all too easy to get those flat ribbon cables in slightly cockeyed to where they make contact on part of the connectors but not all of them. I'd suggest opening it back up and pulling the motherboard again to get to the plug underneath the motherboard.

You see that white line on the ribbon cable right next to the connector? It should look the same as in this picture; an even distance from the connector all the way across; if it's offset then it's not in right. As long as you're there, open it up and pull the cable, then clean the pins on it with some 90% or higher concentration isopropyl (rubbing) alcohol. Inspect the length of the cable for any signs of damage, including tears or excessive bends that could damage the internal traces.

Once you're happy it's all good, plug it back in, making sure it's fully inserted, then reassemble the motherboard. Now do the same with the other end; inspect, clean and make sure it's inserted fully, the same as it appears in this picture.

If it still doesn't work, unplug the display cable from the LCD and plug it back into your original LCD (don't dismount the new screen from the frame). If it works there then it's almost certainly an issue with the replacement part; otherwise you may have a cable or motherboard issue.

Give this a try and let us know what you find.