Hi,
With my laptop I use a vacuum cleaner to gently suck the dust out of the vents, rather than blow it inside. 
Dave
Well, I'm not quite sure which of your pieces of advice did it, but the problem is solved. I ran the scan check a few minutes ago and it went through without a hitch.
Thanks for your patience in seeing this problem to a happy conclusion.
Glad you got things back again.
Did you clean out the vents? If you did, did you notice a lot a dust? That could have been it, causing an overheating problem that would have the computer shut down to protect itself.
I waited a couple of days to make sure that everything is ok. Seems to be, though the area around the fan still seems a bit hot to me. There was one dust ball near it (I opened the laptop and blew it out with compressed air), but the blades of the fan seemed to have a thin layer of dust on them that would not blow off. I tried a cotton swab, but there is not room enough. Do you know any way to clean them? And what kind of solvent should I use? Is rubbing alcohol dangerous?
I would suggest NOT using any chemicals around plastics as they sometimes do not get along. Stick with water and a mild detergent. Obviously the power should be OFF and battery removed. Please be care not to let water enter your laptop.
You can also refer to the manufactures notes for safe cleaning practices
Dave