Know this is an old thread, but have a couple comments anyhow. First, the manual clearly states that the unit will not power on if the battery is low. So, I think we have to wait until the charging light goes off, indicating that charging has been completed, before you try turning it on.
Second, I've had serious battery problems on my sl5500 because of droppage, finally figured out it's just the internal connectors for the AC adapter plug. Will be writing a lot about this in my blog when I can take the time.
So, I'd suggest trying to charge a unit fully using the docking station as an alternative, to see if that makes a difference, especially if you drop your Z while it's plugged in to the adapter.
I'm concerned about their statement in manual that Tosa will not turn on if battery low. That could be serious after there aren't any batteries being made, if it won't even turn on when on AC adapter, if I understand them right, it's planned obsolescence.
sdjf