The LCD cable is the easiest (and smallest) of the three ribbons to snap / click in place. I'd give it several attempts to get the cable connected and if its still showing banding you've either got a damaged connector or a bad screen. If it's an aftermarket screen I'd probably be tempted to go with the latter, but check your board... with a magnifying glass if needs to be. Good luck.
I've had this problem on 3 new aftermarket screens RECENTLY - from different sources. The problem is with touch connector flex. In all 3 cases it's not snapping / clicking on to the board like it should. It also depends on the condition of the FPC connector on the board too. If its perfect / like new you might get away with using these screens. If there are any slightly bent pins the chances of using these screens without any touch issues isn't good.
It's not unfathomable that a third party battery could damage a motherboard. Why not try removing the board and placing in another 5s that you know works? It's the quickest way to eliminate other possibilities? Good luck
Only the ORIGINAL home button will ever work with Touch ID... unless you get it repaired by Apple. You would need to remove the original button from broken screen and place it in your new one to retain Touch ID.
If your screen is acting up (random behaviours - random swiping or random characters etc) and as it's happening on 2 screens, you either have 2 bad screens or: 1. The touch connector ribbon is not connected to the motherboard correctly 2. The touch connector (FPC) on the motherboard might be damaged - remove the screen and inspect it under a good light source If you obtained the 2 screens from the same place hopefully that's where the problem is and not with the motherboard. I've seen a few third party screens coming out of China that have weak touch connectors. They don't snap / click into the motherboard like they should. The main LCD connectors are fine. Good luck
If it's out of warranty I'd open it up and just try reconnecting the home button flex to its connector. If I'm honest, it doesn't sound good if Touch ID is still working for you but pressing the button is unresponsive. As has been said, replacing the home button means you'll lose Touch ID unless its performed by Apple. Hopefully though it could be just a loose connection on the ribbon. If it doesn't work I would just replace the home button, it's obviously better to lose Touch ID than home button functionality. Good luck!
I've had a very similar / weird experience over the past week... So, I needed to replace a broken screen. I did that and I noticed a couple of days later that the flashlight wouldn't turn on in the Control Center. Also, when I take a photo with the flash set to "On" it does not fire properly... The bottom yellow / amber flash fires but the bright white flash does not... I tried reinstalling the screen several times but no go... Several days later the screen started to act up (touch was misbehaving) so I managed to get a replacement. This time, I was real careful, I hooked up the 2 screen ribbon cables (touch + main LCD) and turned it on. Booooom the LED fired right up in Control Center. Awesome, I built up the rest of the screen and assembled the phone as normal, turned it on, NO FLASHLIGHT. Shiiiiiiit tried all sorts, nothing worked so I gave up. A week after that, the replacement screen was also began to act up - same touch issue. So I bought another screen from another seller... Tested the flashlight...