I am getting some clue to what is going on here.
Despite charging for quite a while, the battery pack shows only one bar of charge. And everytime I go to start it up, it fails.
Now - if I remove the batter, and boot up just on mains, it works. And then when I replace the battery, it is actually telling me that there are two bars of charge on the battery.
So it the battery low indicator getting stuck? Could this flashing Scroll Lock be telling me there is not enough charge in the battery to continue?