Fan problem on 5750G

Hello,
I am having a problem with fan in my laptop since monday. Every day happens the same thing to me. When I turn on my computer and start playing a game, after 2-3 minutes my CPU and GPU temp reach about 90degrees and it shuts down. After a short moment I turn it on and start the game and again after 2-3minutes laptop will shut down. But when I am turning my laptop on for the 3rd time I can immadiately hear how the fan starts working just after pressing the power button and feel the air coming out. Every day for 4 days already I have exactly the same problem - fan starts working after 3rd boot. After that the laptop can be on for even 6 hours without the temperatures not coming close to 80degrees even when hard gaming.
I would be very glad if anyone can provide any help or hint about this issue or how to make the fan working always after 1st turning on.

Thanks in advance and sorry for my english mistakes.

I have the newest bios 1.21, windows 7, intel i3, 4Gb ram, nvidia gt 540m

 

Without being able to inspect it, I just wonder if the fan is physically sticking, either because it's obstructed or dirty or the oil has congealed. You might try blowing into the vent, either forward or backward, preferably with compressed air but possibly with your breath or a vacuum cleaner output. See if that starts it moving early.