I'm starting to come up with a curious theory about the cable box, but first we'll take care of the straightforward stuff.
With no trigger cable, you are either leaving the 7125 on all the time or manually turning it on and off. There should have been a trigger cable in the box with the 7125, which when connected to the 990's "Trigger 1" output would let the 990 turn the amp on and off at the same time you turn the 990 on and off.
The power button on the 990's remote is a discrete power "off" command - to turn the 990 on from the remote, you simply pick any input command on the remote (DVD, Video1, ...) and the 990 will turn on and be set to that input. This is done to provide discrete power on and off commands for universal remote users who want to be able to write macros.
It appears clear that you are somehow succeeding in passing HDMI audio through the 990's DVI switching (something that has been discussed in the past and assumed by most around here to not be possible). Here's my theory (and it's just a theory at this point): the Motorola is able to establish an HDCP handshake with your TV that includes successful digital audio transmission, at which point the Motorola concludes (wrongly) that the only digital output necessary is the HDMI connection and shuts down the coaxial and optical outputs. The result is audio from the TV speakers but not from the 990. If I'm right, Motorola has done something supremely stupid that would mess up a good number of home theater users. Presumably in the past the Motorola didn't always recognize the connection (which would explain why the problem only occured intermittently) but a recent firmware update to the box "improved" it so that the box consistently recognizes it. Here's a crazy thought for a test of this: put a
single link DVI to HDMI adapter at the 990's DVI output (something like
this one and then run HDMI from there to the TV. HDMI uses single-link DVI for the video side, and I'm guessing here that the extra pins for
dual-link DVI are what are letting the HDMI audio pass through the 990. If my guess is right, a single link adapter will break the signal path for the HDMI audio, at which point the Motorola box ought to believe itself to be connected to a DVI device and revert to coaxial and optical for the digital output. I'd also take another run through the Motorola's settings before buying anything to make sure there's not some way to disable HDMI audio output - there
really ought to be, even though all indications are that there's not.