It may look like the rectifier for channel 1 is dead. This is the board in the back, containing rectification, filtering and switching between transformer secondaries:

There are three rectifiers; one for each channel. It seems like the logic uses the same rectifier as the actual power delivery, however it's heavily filtered to minimize noise (although one could wonder what badly behaving load it would take to mess up the measurement circuit).
The rectifier for channel 1 has a dead short between phases. You can see it here, together with an important relay:

Now, the relay in question seems to switch between two of the transformer secondaries. If I compare with channel 2, one of them will be connected by default (i.e. when relay is not energized). However, there's not connection here on Ch1, i.e. power doesn't seem to come through. With a second look underneath the board:

That solder joint is kind of odd. Has it melted? Makes me wonder, if the rectifier failed - did the relay perhaps end up acting as a fuse? No power is reaching that rectifier now, that's for sure. I'm crossing my fingers for this, since that could mean the transformer is unharmed and I'll only have to change a couple of "commodity" parts, or at least parts that are easier to come by. The transformer does produce correct voltage on all its secondaries, remember.
Oh well, time for bed again, be back tomorrow.