This is really good stuff I have seen the issue with the different connectors and that its self is a big problem, send it back I found this seller on ebay and never had one problem with the white screen, black screen again, I own my own repair shop and been doing this for quit some time now and had this problem many times, run the battery out recharge, always on the connector that is on the underside use a bit of the 2mm double side tape after it is seated, when you replace the board back in it comes loose, that is why when you first open it up it has the copper heat sink tape on it not only for the heat but to keep it sucurely in place, I also use the amber heat shield tape to hold the top cable down securely because when u move it just a bit putting it back in it can wiggle loose, thus the white screen. The ebay seller I use is
Hudson_River_Goods (10360) $24.45 in the 3 years of dealing with them never a problem with the white screen, make sure its off before you start, be care with everything, and dont heat to much before or after, heat will also cause these cables to be unstable at the screen side do to they are not soldered to they are heat pasted soldered thus heat will loosen them. The guy above with the pic showing the difference in the connector is right, one is for the begining ipod in the that gen and the other is for the later in that gen, if you go cheap you get white screen use the seller I told you about and you will be just fine, good Luck.
Thank you and Good Luck