It seems there are many folks with the suspend of death on the NUC. When you suspend to RAM you can't get back. When you disconnect power for a while you can't turn it on again. Welcome to brickland, population: you. I found that following the advice on the forums if I disconnect the CMOS battery for a bit then I could turn on the NUC again.
Luckily I found these extension leads which let me bring out the battery from the case. So hopefully now a debrick isn't going to involve a system teardown anymore.