New Macbook Pro won't restart after migration assistant.

Ran migration assistant from an older macbook pro (ethernet) to the latest 15in model. Left it going, overnight, with 3 hrs left on the clock. The next morning, the old mac screen was asleep and wouldn't wake. The new screen was black-glowing (so power, but no image) and also wouldn't respond.

I held the new mac power button for 5 seconds and it switched off, but now it won't power on.

I've held the power button for 5 and 10 seconds and there's no sign of life.

What should I do? After a search, I see I'm not the only one to whom this has happened, but I couldn't find a clear solution.

Thanks for your help;