Replace the battery is the first step to do. Then, if still not working, should be IC or water damage.

The tech who replaced your screen broken it again. There is no other option if you have grey line in your screen.

If you can't connect to a cellular network on your iPhone, make sure that cellular data is on in Settings > Cellular*. On your iPad, go to Settings > Cellular Data. Reset your Network Settings. Tap Settings > General > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before. Try updating your phone. If still not working, it look like water damage. Even you think there is no water damage, note that only small drop of rain water can enter in the device and make corosion. But anyway, i would suggest to take a look to SIM tray as last.

Any help please :( ?

Please help me i really need to know :(

Make a restore of your iPhone before doing anything... And it look like you are looking for this post: battery draining, and missing components near the battery connector

Wipe all data factory reset

The LCD is broken. You have to replace it.

You are in DFU mode. To exit DFU mode, press home button and power button in same time for 7 sec, then release the power button and still pressing home button until the iTunes logo disapear.

Corrosion. You only way to MAYBE fix this, it is by using isopropyl alcohol on corrosion on motherboard.