Originally Posted by
peterb
If that is so (and this is only a theory) possibly an internal power supply problem with the battery monitoring and charging area. The on/off switch is a 'soft' switch so if there is a problem with the circuitry associated with the battery, it could prevent it from poering up. Plugging in the mains adaptor circumvents that aspect of the start up - but once started the battery will run it successfully.
If that is the case, I'm not sure that there is much you can do to fix it.