If my iPhone screen went black/unresponive, will a replacement screen kit fix it?

Everything still works fine. I just dropped it and now mine screen is black. I wasn't sure if the replacement kits were only for cracked screens.

Also, if not, will a replacement place fix it?

It depends what kind of replacement kit you're buying.
If you find that repairing it it's too expensive I would recommend selling it.
There's a great website that buys used and broken electronics. And they offer best prices on the market.
Check for yourself - http://sellbrokenelectronics.wordpress.com/