well that LCD works in ALL 2nd Gens and 3rd Gens. So might be an obstruction in the LCD port where you plug it in causing a short or something. I would suggest blowing that area with a air bottle and inspect the ribbon on the end just to make sure its clean. And if same issue try to attempt a DFU mode restore and see how it goes.
LCD and Digitizer are fused together and it is not recommended anywhere to do the fusing your self. I would suggest to return your items and buy the fused lcd and digitizer as that is the factory OEM way.
If you have a small paper clip you should be able to put a really small amount of super glue on it to fit in the dead center hole in most common headset male connections. Let it dry for 10 minutes then should be able to pull it out. had to do that on a htc phone when a cusotmer dropped it and it pulled out just fine. That is the simplest without having to worry about damage. Some will use a dremel tool to put a hole in them and put a tiny screw in the hole they made. Some ideas but this should do the trick
Well here is some ideas as it is hard to troubleshoot your device with out seeing the symtoms myself. iPhone will reboot itself if it detects a hardware issue. If the iPhone has never been taken apart before I would like to say with a high percentage that the logic board is defective. Lower percentage is that there is a loose connection, liquid damage, or a simple short in the system. Just some ideas to throw out there that should lead you to a full complete resolution
If you have checked that the ribbon is secure and that there is no damage anywhere on the ribbon attempt to restore the ipad using DFU Mode and if that fails then you most likely have a defective touchscreen or the soldered in adapter for the touchscreen is defective.
The White screen is famous when the cables where not properly installed on logic board. check your connections. If the everything is in place and same issue check the cable ribbons for any tears, dents, or any damage to the ribbon cable. If the cables look fine attempt restore or DFU Mode Restore and if those fail you might have another issue which is more costly. Check those and if none of those most likely you will have to spend money.