I managed to "fix" a 3DS that was exhibiting the exact symptoms as in Andrew's fault description. I followed oldturkey's advice and opened up a 3DS I bought recently. The unit was sold as faulty, and I could see from the wear on the screws that it had been opened at least once before. The fuses checked out ok, so I put it all back together. The iFixit guide doesn't mention it, but some of those ribbon cables are a real pain to get back in (I recommend some rubber-tipped tweezers!). Anyway, long story short, the unit starts working the moment I have it all back together. I'm therefore assuming that: (1) A previous repairer had failed to get those ribbon cables connected up properly, or (2) The unit had received a jolt at some point that had dislodged one of the ribbon cables.
