typically the issue you described would be the logic board as you suspected, but if a new board does the same thing that is quite weird. Generally on that model if the screen goes out, it ends up being the LCD itself, but if it doesn't work on an external, that most likely won't be true. For the DC-DC board, the machine usually won't turn on at all if it is bad. If you are wanting to fix it yourself, I would probably go with the DC-DC board next, but I'd really recommend taking it somewhere to get diagnosed at this point so they can switch out all the possible parts without you having to keep ordering them yourself and sending them back.
we do offer a free diagnosis here if you don't mind shipping it off, and if you decide for us to not fix it, you'll only be required to pay the shipping costs.