Ouch! I was hoping it just went flat dead which would imply the power supply. Using a meter you could verify this by checking the DC lines. With better detail on what happened it's clear the logic board did go on you. So doing any testing won't help.
I would first go back to an Apple Store with your paperwork showing when you bought the system hopefully you can do this ASAP.
Plead your case with as sad face you can and don't take no from the first person. Ask to speak with the support manager to see if they can still cover it under warranty as its just so close in the expiration date. If they still say no see if you can get them to cover 1/2 the cost but hold that for the last. If you have a second Apple Store near by give it a try if the first fails you.
Remember to try getting to the store early before the staff has been worn down for the best results given the season (Black Friday weekend).