I think being unmotivated and a headcase are two separate things. I'm a Blake fan, and it would be hard to argue that he isn't a headcase. The five-set record is the best example, but there are others such as a tendency to choke, going into deep slumps, and an inability to perform at his best in important matches/tournaments.
However, I don't think this means he is unmotivated. He is generally very intense/competitive on court. I watched the finals of the 2008 Houston tournament recently where Blake lost 7-5 in the 3rd to Granollers. At the end Blake was noticeably very disappointed (and this is Houston we're talking about). I think many of his comments, such as the one you mention in the first post, are meant to come off as humble. I think he generally does feel lucky to be playing tennis at this level, especially since when he was a junior he never imagined that he'd be playing pro tennis. Hell, he considers himself lucky to be able to play at all considering his severe neck injury in 2004. Him getting down on himself in matches is more a result of an inability to control his emotions, which are primarily a result of frustration if he's not playing well. That's him being a headcase, not unmotivated.
But when he's on that forehand is one of the best shots in the game in my opinion.
I know he wants to win, but I just feel like if he was locked in some intense battle he can rarely find a way to pull through. Its partly nerves but I think he also just doesn't want to win as much as his opponents usually. I've seen him play amazing tennis, but he never seems to play his best at the critical moments. Maybe its motivation, maybe concentration
but the top players play their best on the key points and Blake seems to consistently choke