Finally had some time to look at this boy. 
I tried Elfen's suggestion and scrubbed the board with alcool and a toothbrush, but it doesn't seem to have made any difference. I also cleaned the internal structure just in case, but to no avail.
The symptoms are pretty much the same: if I plug the power supply first, I hear a scratching sound coming from the speaker, but the green light doesn't turn on. If I unplug and replug it, however, this time the green light turns on and I still hear the scratching sound - but the system simply ignores the power button. 
Resetting the machine with the reset button on the rear seems to produce similar effects.

I've now tried cleaning the board with both acetone and alcool - will report back as soon as it dries up.