If you've dropped your G2 (as some in this thread have already mentioned), even from a relatively small height (e.g. 6 inches), this is likely to be the cause. I had the same issue with mine, purchased 10/2013, with what I thought was a knock/drop not worthy of mention, at least, not compared to the abuse my previous iPhones and Galaxy 3 were subjected to with no resulting failures. I found that twisting the body of the phone got it to work intermittently and for long enough to allow me to back up the data before sending it to LG for repair, which they did with no objection as it was under warranty.
I'm not recommending twisting the phone as a solution, but rather to demonstrate that the physical force made the screen display properly again. This would correspond to those who said pressing the power button or other forceful actions solved the problem. I too thought it was to do with the power button until that stopped being effective. Basically, it appears that something gets disconnected, with regards to the screen, quite easily e.g. with a small knock or two . It certainly wasn't a software issue. The description of the fault by LG's repair centre was 'Screening', and the symptoms were as described in the original post here.
The UK warranty for this phone is 2 years (meaning that any phone with this problem at time of this answer being posted will still be under warranty and should be sent direct to LG - register on their website and initiate the return there), but I can't speak for the US.
In terms of fixing it yourself, you can try and there are videos on YouTube that show people dismantling the G2. Taking it apart alone didn't look like a job for the faint hearted (and I'm a fairly confident fixer), so check your warranty first. Other than that, twisting, pushing or otherwise forcefully manipulating your phone may solve the problem periodically, but trust me, it's no way to live!
I love the G2 (I still have it), but it isn't built for hard knocks.