If you are experienced, disassemble the unit and look for any loose connections or broken components. If any of the solder joints has cracked or broken though (eg, under the Northbridge), then there is probably nothing you can do about it but to get a new motherboard. If you have important data in the laptop i would suggest to make a backup before attempting anything else. In case you wonder how to do that since your laptop is not working, take it to a computer store, where they will take the hard drive out, backup your data on another medium and you are ready!
Its possible the power cord was plugged in and if it was dropped, or nearly dropped but caught, the power cord could have applied pressure to the adapter soldered to the motherboard and the connection was broken and now you are getting a power on/off effect.
My first guess is something to do with that adapter the power cord plugs into. Even if it wasn't dropped, these sometimes get pressure applied to them from the cord and it loosens the connection of the solder and breaks the connection.
Some places can fix that for 125 bucks but they wont guarantee it will work. I have had a few laptops like this and thats almost always the problem...