Are you sure it isn't overheating?
During the first several monthes of getting my new laptop, I would be able to play like... 3 games on my laptop without it overheating. But sadly, quality goes down over time.
Every time my laptop turns off from overheating, it does what your laptop does. All the lights turn off, including the battery and adapter light, and I wouldn't be able to turn on my laptop until the adapter light and battery light came up, which might take only 5 minutes for me. And it overheats faster than last time and takes longer to be able to turn on, etc.. so after all those 'overheat' incidents, my laptop will shut off on me when I'm playing games like Trickster.
At first, I thought it would be the battery's fault, but eventually I came to figure out it was because of the heat.
When your laptop randomly shuts off, feel the bottom of your laptop and tell me how hot it feels. If it's hot, it probably means your laptop overheats easily just like mine (Toshiba brand laptops tend to do that)
I solved this problem by getting an external fan for my laptop. After getting proper ventilation, I haven't gotten a single 'sudden' shutdown on my laptop for over a year.
If you need a picture of what it looks like, I have one o.O
Just stick it under your laptop o.O