From your description, it sounds like your power supply has failed and no longer charges the battery. Do you see an orange LED indicating the battery is charging, or a green LED indicating the battery is charged? Or no LED?
If green, I would open the bottom of the laptop and attempt to reseat memory and HDD(s). I've heard of this bringing a dead system back to life from threads in this forum.
If you just got this system and are in the retailer's return or exchange period, you may want to consider that if the above fails. If you are beyond the return point, you may need to prepare for an RMA:
http://rog.asus.com/forum/showthread.php?7004-ASUS-ROG-Support-Guide-and-RMA-Procedure-READ-THIS-FIR...
G74SX-A1 - stock hardware - BIOS 202 - 2nd Monitor VISIO VF551XVT