It sounds like you may mean one of the two contact prongs which are part of the Charge Port Assembly. If that's the case, if you know how to solder, you can solder something there in lieu of the prong... or you need to replace the charge port assembly.
How are your soldering skills? The only real way to fix it is to cut the entire plug off, get yourself a new jack of the same size, and solder it on. If you don't solder, there are people around who can do this for you. It's a fairly simple job.
Part of the cables on these screens need to be adhered back onto the digitizer before plugging in. If they weren't adhered, then they would appear far too long. Your home button connector on the motherboard may be damaged. Or the cable not plugged all the way in. Or if you purchased a screen with a home button pre-installed, then it may be faulty. Unfortunately, the only ways to do a reset is to allow the battery to drain to absolute zero (which could take forever), or open it back up to see what's going on. If the home button connector and cable all looks good and you don't have a spare to test with, the other way to do a reset is to disconnect the battery briefly. Be careful though, as the motherboard is held down with adhesive.
Unless you have experience in glass only replacements with these types of screens, replace the full LCD/Digitzer Assembly. The glass, digitizer & LCD are all glued together and it is VERY easy to damage the LCD and digitizer in the process of removing the damaged glass.