It sounds like you've done pretty much everything you can do on the hardware side of things, but it's a little difficult to say exactly what the cause of the problem might be.
Where do you have your laptop plugged into? Is it straight into a power socket or going through an extension/4-bar socket? If it's in an extension socket try plugging straight to the wall socket and see if that makes any difference? The other things you could try are a little trickier, such as reinstalling Windows, etc.
It could well be a hardware issue too, of course - so you might need to RMA it in the end.
Asus ROG G751JT-T7115H
17.3" IPS, Intel i7-4720HQ, 16Gb RAM, NVidia GeForce GTX970m, 256Gb M.2 SSD + 1Tb SSHD