It is possible that it crashes during bootup when it is not plugged in because the battery is not supplying enough voltage to meet the systems demands. How old is your battery? Do you do a lot of really taxing stuff such as 3d gaming or video rendering on your laptop? If you do do a lot of other very intensive stuff and the problem does not occur at those times then this is less likely to be a problem.
Yes, but no sprinkles. For every sprinkle i find, i shall KILL you.