Sorry to be a downer, but Apple will find out if the screen is a replacement screen eventually. But yeah, I'd give it a shot.
Perhaps you ordered a faulty screen. The aftermarket products you find online usually are not as good as their OEM counterparts.
I'm just thinking out loud here, but I'm guessing it can't be the ribbon cables if it turns on and stuff...
The only other possibility is that you purchased a bad screen.
One thing I would suggest is to test your original (damaged) screen on the unit. I would definitely exercise caution and limit how many times you take the thing apart. But if you do believe that the new screen is a-okay and that your unit has problems, try the old screen out.
If the old screen works perfectly, though cracked, then you can conclude that it's the new screen that has issues. If the old screen has the same problems as the new screen, which I can't see happening, then something's wrong with the unit.
Cheers and good luck!