I've been having the same problem, but it has happened so many times, that it might cause serious permanent damage to my computer.
I start off the game fine, then at around 8-12 minutes into the game, everything stops and my computer turns off. When I try to get back on my computer, it starts up for 20-25 seconds then turns off again. When I can finally come back on my computer without crashing, I get back into the LoL game, but there is a 50/50 chance I will actually be able to stay on for the rest of the game, or I will have another surprise shutdown.
Note: I tried to play a LoL game yesterday, and I got another "surprise shutdown" after only 2 minutes of the game. I tried to log back on my computer, and I had a fatal error and it wouldn't start. Only after a few hours, I turned it on again and my computer turned back on.
Note(2): I am playing on a HP Compaq Laptop, My processor is an AMD Athlon Dual-Core QL-64; 2.10 GHz, I'm running on a 32-bit laptop, and RAM is 3 GB (2.75 usable).