My laptop appears to be well and truly broken; when I turn it on it'll start up very briefly and the fan will blast uncharacteristically, only to turn off within 5 seconds. Then after waiting for a few seconds it will start up again, the fan blasting out again only for the screen to remain blank. I should mention my screen isn't displaying anything whatsoever.
My laptop has never had any noteworthy issues. The model is a HP Elitebook 6930p
The fan blasting is usually an indicator of overheating - it could be from a defective fan, or dust inside the laptop. It could be as simple as replacing the fan and/or heatsync (re-apply thermal paste). Usually that is a $20-$30 repair.
Hmmm it's not two years old yet, but the model is 2009 I believe. I bought it refurbished. You mention the overheating and that's what came to mind. I suppose my laptop thinks its overheating (I have software that manages this).