Could be any number of things but my best guess is that the CPU fan has packed up which would produce exactly what you describe. If the fan doesn`t start the computer will cut out as a safety feature to prevent damage to the processor from overheating. The fan may simply be clogged with dust which prevents it from spinning.
Is the laptop plugged in to the mains?
Try this - remove the battery and unplug from the mains. Now hold the power button down for about 30 seconds. Now plug it into the mains again without the battery and try to boot up.