I think the only thing the stylus gains you is a more postive pressing of the power button. That is not however a factor in wether the device boots or not. I do believe there is a time factor that you need to wait for the lights to come all the way (4 seconds). Ive seen some discussions about booting up with two quick presses being different than one long press, so that supports that it's significant.

This powerup issue is more complex than people not holding the power button down though. I've used mine for almost two months before I began to have the problem.