Flea power is the common cause to this prooblem, basically what happens is when residual power that remains after the computer is switched off interferes with the system preventing with the boot process.
'''What you do'''
# Turn remove the battery
# disconnect adapter
# Press and hold the power button for 30 seconds
# Connect the power adapter without the battery
# Your computer should turn on now
If it doesn't this [http://accatech.com/dell-inspiron-laptop-wont-turn/]has more technical details, it might be about a dell laptop but i have used the same tips on other brands like hp and asus and it worked