iPhone 5 battery percentage will not change

Hi. About 4 weeks ago my screen started coming off the front of my iPhone 5. I thought nothing of it and I opened it up to see if the battery was ballooning because I heard that can cause it, but it was fine. A week after this, I decided to disconnect my battery and reconnect it again due to it going flat at about 60%. After this, my iPhone started rebooting itself every 3-5 minutes and every time it came back on the battery percentage would change dramatically. And I also noticed that the battery percentage would not change unless it rebooted, or I turned it off myself.

I purchased another battery so I could replace it because I thought it was the battery causing it. But I replaced it and it still continues to do the exact same thing. I have restored it and everything. When I purchased the battery, I also got a new rear housing case and screen because my housing case was pretty bumped up and I just thought it'd be nice to have a neat one, and I also got a new screen because the glass on mine is coming out of the frame (as I said before). My screen has not arrived yet but the housing did. I replaced the whole housing and put the new battery in again but I still have the same problem.

So I've pulled the entire phone apart, restored it, updated it and replaced the battery, what more can I do? Well, I was thinking it could be my screen because when it's about to turn off the screen gets lines and different colours on it for about 2 seconds, then turns off. Just like when the LCD plugs aren't in correctly. AND due to the fact that it started happening when my screen began to come off. I don't know if this could be to do with the battery or screen or anything else, because I'm not an expert. I'd just like to know if the screen could be the cause of it. I don't want to take it to an Apple Store so any help to do at home would be great.

Also while I'm on, i have a small problem with my SIM tray. After reassembling to the new housing case, I just screwed the small lever piece back on (the one that swings when you push the eject tool in to pop the tray out), all it does is pivots around and doesn't trigger anything. If anyone knows of any connection I have forgotten or anything, please help!

All help is appreciated :)