Based on the huge amount of the complaints with the same problem; G751JY connected to the main power, but not charging, is definetely a design flaw ASUS is not taking responsibility. You will be instructed to send your laptop to ASUS repair, that will cost about 700-1000 USD, where the main board and possibly the AC connector will be replaced. I've almost walked this path, but eventually dumped my 2000 USD laptop after 2 years of usage. Based on some forums, the failure will might return after some time.
The problem occurs when nVidia GPU switches to the PWR mode, taking current both from the battery and AC. This completely disables AC and you are not able to charge before the machine has cooled down, in some cases, even not then.
Sad thing is, there is huge amount of people suffering this problem and it gives really bad taste of ASUS product line + there is no DIY fix for it.
