Ok, I've done some further tests.
So I've tried to power-on with test leads, no problem whatsoever.
Selftest runs for about a second and everything works fine.
I've even gone into the "utility" menu and manually launch a self test, no problem.
The DC supply can act as a squarewave generator, so I've given it a try.
I set it to 1.5V (squarewave peak-peak from 0V to 1.5V), at 480Hz (around 2ms period), with a 25% duty cycle.
As you can see on the attached picture, except for the noise, it works fine.
I've checked by feeding the output to the DMM input, readings all fine. And double checked with my Fluke handheld.
I'm puzzled