Just bought the laptop 1 week ago; battery charged (fully) will power up laptop stays on for about 10-15 seconds and then shuts off. Connect the power cord and power on; the same issue happens. Pulled battery away from laptop and re attached and tried the power up; same thing happens the laptop will shut down after 10-15 seconds.
If you just purchased this laptop (assuming it is new), you have a warranty. Return it to where you purchased it. That type of problem in a very new system is not a good sign, probably a weak component that passed initial testing but failed soon after you began using it regularly. If at all possible, get them to REPLACE IT with a NEW one. You purchased new, you should get new (not to repair that one and definitely not a refurbished one [a repair of someone else's defective return]) You have to be a little bit crazy to keep you from going insane.
If all else fails, read instructions.