My computer shut off and hasn't powered on since

Hi,

Did you try the procedure of removing the battery and the adapter, then pressing and holding the Power button for 15 seconds then releasing it then reconnecting and turning on the adapter only (leave the battery out at this stage) and seeing if it would turn on?

If so and it still didn't work, then given that you have had the laptop for less than 12 months, I suggest that you consult the warranty documentation that came with the laptop as to what you have to do to make a claim for a warranty repair or replacement.