Do I need to replace the whole logic board?

As the title suggests, I have a problem with, most likely, the logic board. The iPhone is a 5SE. About a year ago the battery started dying, as in, it didn’t have any more “life” left in it. So we put it somewhere on a desk. After a few weeks, I noticed the screen was pushed upwards a little, indicating the battery was inflated. However, we ended up replacing the battery about 4-6 months later. As we removed the old battery, we noticed it leaked at some point. But we went ahead with the battery replacement anyway. Well, here are the problems:

1): You plug it in, and a few seconds later it tries to boot. By “tries” to boot, I mean that it will show the apple logo, stay on for a few seconds (about 3-5 sec.) and then shut back off. It will keep doing this for about 2 to 3 minutes (sometimes more), and then it finally boots, and starts charging. This is where I thought I fixed the phone.

2): It, as mentioned above, turns on (eventually) and then seems to work fine. You can do whatever you want on it, as you should. But then, after about 3-5 minutes, it shuts off, and repeats the booting process, until it turns on again. This will happen over and over and over again.

3): We ended up trying to put it in DFU mode, which in the end we succeeded doing, but nothing really changed.

Important things I have to mention:

#1: The battery percentage usually changes from 1% to 100% every time it shuts off and reboots.

#2: The leak did appear to end up near the PMIC, although it wasn’t directly under it.

#3: As you can probably tell, the battery percentage reading is incorrect.

And so, in conclusion, my main question is: Should I replace something in the logic board or just get a new one? I think it might even be a short circuit somewhere, although I did not test that. Maybe it just needs a good clean? And, lastly, could it be the PMIC? (Although, I know that is an unlikely thing to get damaged).

~ Thank you for reading, and I appreciate any input! I hope it wasn’t too long Of a read.