I know this is an old thread, but I found it useful and hope an additional post will be helpful to others who find this thread after me. I recently experienced a problem almost exactly the same as the problem described here. Green light on power adapter lit while using the laptop, received a message that I had 1 minute left on my battery (even though laptop was plugged into power supply), computer died within 15 seconds, and would not start on power supply, would try to start on battery, but battery was depleted. I chatted with Asus online and was told to take computer to 'Geek Squad' for service. I do not care for Geek Squad and requested an RMA, received one. Checked with Geek Squad anyway, they looked at my G74SX and told me it was too old for them to service. This made me hesitant to send it in to Asus for service (not cheap and shipping would be on me). Ordered a new power supply from Amazon (far cheaper than last time I had to order one), received it today, plugged it in, problem gone. I am very relieved. Have owned this fantastic laptop since new in 2011, and the power adapter (this new one is the third) is the only problem I have ever encountered with it. Most of my data is stored on external drives, but some of my proprietary software would have been difficult to recover (have to find current vendor, verify product numbers/keys/etc). I hope this helps someone who is as frustrated as was I. FWIW, I run a dual boot (Linux/Windows 10) on the machine. Good Luck!
Caruso