This is a quirky little problem I have... I still get to enjoy my lovely little freebie baby, but one day I'd like to take it out!
Basically, the first thing is, it only seems to boot when the mains wire is connected. I did try buying a new battery but that didn't solve it (although did give me more life - the old one was RUBBISH!) The initial lights come up, you get a hint of a whir, then it gives up.
The second thing is, even WITH the mains connected, he only boots on the second attempt. i.e. I power up, I get the lights and little whir, then nothing. Then I have to hold down the button power to shut down, and then power up again. The second time everything is fine.
Although.... very rarely... once in a blue moon and only once or twice it WILL boot without the power cable and on the first try. Beats me!!