No. Windows reinstallation did not help. Emptying the PC of everything did not help. Updating all drivers did not help. I am still unable to play WoW; the machine keeps shutting down after a minute or a few. Guildies and friends have offered me help in our Facebook group, which is much, much appreciated. However, it looks like I will have to take the machine back to where I bought it, as it is likely an issue with memory circuitry. And that means I will not be playing WoW for some weeks, probably not for another month, since I will be abroad from the 9th of April till the 24th.
Although the machine runs WoW and other games well, I am certain I will never buy a laptop again. I wouldn't have bought one last time if I hadn't had the need. I had to change my location every now and then, and a laptop was the obvious choice. However, my next computer, which will likely come around in late-ish 2014 or early 2015, will be a proper gaming computer.
So, this is just a little update about my situation regarding gaming equipment. I will pop around with more news and WoW-related posts even during my absence in the game. Have a fabulous spring if you are in the northern hemisphere. For people in the southern hemisphere I wish a fantastic autumn. If you only experience two seasons, I wish you an excellent either of the two, probably the rainy one.