Okay, now this is pretty weird, I also have a G73JH with the ATI 5870m, the exact same thing happened to me, it was about 1:00am on 4/19/17, I was playing World of Warcraft when my graphics just went out, screen just turned into vertical lines and so I forced a restart and just like you described my screen would freeze, the mouse wouldn't work, but no blue screen.
Sometimes it would freeze before i could sign in, other times it would freeze when trying to start a program, eventually I just re-installed Windows 10 and right now are working on getting all my drivers back up to date, I'm using the ATI Crimson Beta from 2010 to see if that helps with the issue, but if you had this problem, and I have this problem, this is a software issue, but what... I have no idea.