Microsoft barely broke even on the 360 console mainly because of the $1 billion they had to dish out to extend warranties and etc for the ring of death issue (at least they recognize their fault and did the right thing). If not for this they would have turned a huge profit on the 360.
I own a 360 and never even thought about buying the HD DVD add on, I was actually very happy that it was just an add on and didn't force me to choose sides like the PS3 did (which is also the reason I bought a 360 instead of the PS3).
MS backed HD DVD because it uses VB scripting versus Blu Ray uses Java scripting, I'm fairly sure that competing with Sony/Blu Ray was not that high of a priority.
HD DVD loosing is definitley not a good thing for MS, but it is not by any means a 'nail in the coffin', making the HD DVD an add-on actually saved them.