Since you ordered a new charging dock, try to overlay it over the exiting one in your iPhone, connect it, and short the 2 golden prongs of the home button like Patrick said (they are at the end of a flat cable, included in your charging dock assembly).
If the home button function works, try again with the old charging dock.
If it works too, the issue is with your home button flex cable not working or not making contact with the prongs.
If neither charging dock work by shorting, your issue is further down the line, on the logic board. At this point, you need to use good magnification (10x is a minimum, 20x is ok) to examine all visible parts of the logic board, especially around the battery and charging dock connectors. If you see anything damaged, part broken off, or missing, try to upload a good quality picture and we'll take it from there.
Good luck.