Does this one have the battery option? ... if so, I would take a look around there.
Otherwise, this sounds like a problem that often afflicts laptops. But you're saying that the power supply is OK. Are you sure that the voltage doesn't drop down (or out) when starting up?
Myself, I doubt that major components are at fault ... more likely to be loss of battery-backed start-up parameters (NVRAM, or whatever) - or even dust or (and) fluff!
