Chosen Solution
Sound like a long screw damage, did you maybe put the wrong screw in the wrong hole when you were putting on the LCD shield?
The battery that you purchased either came faulty or the battery cable just got twisted and the battery power line happen to be broken internally. Upon such, you will have that issue. You can try with the original battery and see if you iPhone is in good health. I don’t think that you discharged static over the logic board! You can still return the battery if you believe that you didn’t poke the battery cable and your iPhone boots up with the old battery. I suggest you to get better battery here. They are safely packaged and safely boxed.
You might have damaged a filter very near to the fpc battery connector of your logic board. Look closely (best with a microscope) if one of those tiny components got ripped check also the area where you doc connector fits into. A missing/ripped or damaged filter, can cause a phone to not boot properly or not at all.
