Thanks ken_yap for pointing me the right way. I did select repair system from the installation dvd and nothing strange was reported, so I guess my disks are still healthy. However I did not like the repair system option very much, since I don’t know what is that autorepairing do and how. Probably it does everything as it should and I don’t need to worry about that, but still I and probably also someone else would like to know how to manually do disk check. My problem is solved, but despite that a good explanation for others having similar problem would be very helpful.
So first I decided for the second option that ken_yap suggested, that is to boot from installation dvd and select Rescue option, which put me into comand line interface (CLI) and from there I tried to issue fsck command, but the result was that it printed out the version of fsck (V 1.41.11 or something) and did nothing, I saw no processing of my disks. I think this is very strange or it may be, that if the disks are ok, it doesn’t say anything else but print the version number. But that didn’t convince me, so I decided to try the third method. I rebooted pc and on the grub menu entered “1” (without quotes) and pressed enter, this put me in single user mode on run level 3, after root login I tried to remount all partitions with commands like
mount -o ro,remount /dev/sda1
which worked on all partitions except on the one running the kernel, saying the partition was busy, and I was back at beginning of the story. Afterwards I decided to use autorepair option.
I would be thankful if someone would briefly describe the correct way of doing fsck, or tell me which mistakes I made during my attempts. I’m not much experienced penguin yet, but am willing to learn 
Thanks for help again.