Ok, so recently my STE had been missing the green channel completely. I thought this was my DIY RGB cable, so I ripped it apart and re-soldered it (I actually meant to test it first, but it was such a poor job the ripping apart happened as I disconnected it... those 13 pin DIN plugs are tricky to solder!). I tested it after resoldering it and continuity mode of the multi-meter was all good so I hooked it up and powered on, alas, still no green.
Figuring there may be a bad solder joint on the connector on the board I took the machine apart but nothing was obviously wrong. I powered it up naked, with just the display attached, and sure enough, I got a TOS desktop in full colour. Ok, let's put it back together. I put on the annoying as hell back plate and put it on the base of the RF shielding, then figured I'd test again before going any further and that's when it seemed dead. Took the crappy panel off again, put it back down naked, and still blank. There's an occasional flash on the screen toggling the power, but that's it. I can't see anything obviously bad on the motherboard, and have given everything in a socket a gentle prod or two to no avail. The CPU felt pretty hot after a short while, but I'm not sure how hot they get in use.
Where's the best place to start diagnosing this? All the caps look good, and the power supply is putting out 5.1 on the two 5v lines and 11.8 on the 12, all holding steady.