If the fan is spinning when you switch on the laptop and there's no display, this can be a problem with the memory. Try removing it, putting it back and also if you have 2 memory cards try with only one (alternating between RAM slots to establish if one is faulty).
You can also try this:
Remove battery, unplug power, hold power button for 60 seconds, turn on computer with power plug only, then shutdown, add battery and restart