Is it my Logic Board?

About a month ago, my iPhone 7 started acting funny. The screen goes black, often with a thin, horizontal line of pixels still illuminated for a moment, then it shuts down completely. If I keep it plugged in, it will boot up and stay on for anywhere from a second to 5 minutes, then it will do the same exact thing. Each time it boots up, it charges a little more. I've been able to charge it to 100%, but it would reboot hundreds of times to do so. I've since replaced the battery and lightning jack. Still the same thing. Could this be a logic board issue? I don't care about paying for a new phone, but I have important work data on the phone that I MUST get. I need to either fix it, or get the data off. Any ideas will be appreciated.