Open your iPhone, unplug the battery, plug it back. It will be fine. Only do it if your password is never changed and you know that it is correct. You will be fine.

The touch screen needs the replacement. This link has most helpful answer so far. Hope it helps.

Considered that display is not failing, restoring to factory defaults may resolve this issue. If the issue persists even after the factory restore, it may increase overtime and a display replacement is inevitable eventually. Before restoring to the factory defaults you may consider hard resetting it. You may press the home and power button at the same time while the phone is turned on. As the pone turns off and then Apple logo shows, let go the pressing of power and home quickly. If this didn't resolve, I recommend you to attempt factory restore. You would also like to check how much space you do have in your iPhone. If you are running out of space, prefer deleting some not needed contents. If it is most definitely the display issue, you can have it here at fraction of the repair cost. Hope it helps.

While restarting, click Command + R. When you are at Recovery Utilities, choose Reinstall the OS X. If reinstallation is not permitted then you would like to erase the existing OS X from Disk Utility. Do it only if the data is not important. If data is important, you may first put you Mac in target disk mode, connect it to another Mac (if available) and save all the data important. If reinstallation or fresh installation of OS X mitigates this issue, you are fine. If not, your top-case with keyboard seems failing. (In some cases like this I have seen Logic Board failing). How to figure out if the topcase with keyboard is failing when you do not have replacement parts in hand? Well, you can open the back-pane. Turn on your Mac and quickly, lift up the keyboard latch and pull the keyboard flex out. Let your Mac run without the keyboard and see if it turns off on its own. Do not let it sleep. Keep waking it up using the trackpad. Upon keyboard disconnected, if your Mac still turns off, it's not a keyboard...

When the dock connector malfunctions it stops taking charges. Up on such, the dock connector assembly replacement is the only solution. You can get a replacement part here and the replacement is fairly easy.

The backlight is integrated to the display layers. The display is a single block that is beneath the digitizer. And the digitizers is also known as touch screen. The backlight is the main agent that lights up the layer on which we are able to view stuff displayed.

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.

Getting great battery is quite difficult. Most of the sellers are found selling low quality battery. This is the reason the replacement battery is not any better than the old one. I suggest you to get better battery something like this. There are no batteries better than I suggested. Most of the time I purchased batteries for iPhone 5S and iPhone 5 came mostly dead or poor in performance. I had to return a few times. This seller is maintaining so far. Still I can see some not quite satisfied instances. In my personal experience, these are quite well.

The camera and the flash light are correlated parts. If camera stops working, the flashlight doesn't work either. Therefore, fixing camera issue resolves the flash light. You can get the required part here. Check out similar vendors selling the same items at the most competitive price. This will benefit you.

You can get a replacement screen right here. Once you get it, simply take it apart with the provided tools and replace the screen carefully. You may like to watch a youtube video on how to. That will be helpful. If you are not quite sure about it, you can ship your iPhone to a service shop like this one if you do not have one in your local area.