Hi!
I've had a similar problem with a E6420, fortunately it was not the main board, but a secondary one that needed replacement. I know that you have a different model with a different board layout and that yur problem is with the main board, but hopefully this confirms the theory that this problem has been there for some time.
Now about a possible fix: I too tried fixing the thing with some board level repair: I unsoldered the faulty USB port and replaced it, but the new one did not last, then I replaced the board. If you try to do the same, I believe that you will get similar results as me, that's why I recommend replacing the motherboard entirely.
Finally, I still believe that replacing the motherboard is a better option than buying a new laptop. Hear me out on this one: the hardware inside is already 4 years old (not saying that it is slow or anything). You will probably want to buy a new one within the next couple of years, so in the end it is better to save those 1-200$ now towards a new model than shelling them out now.