Here's what I think about the situation.
I'm sure, I haven't got any problems with BIOS, the motherboard or other hardware. Also, I think that the problem is in the fsck utility. It seems, it can't perform an HDD check. Early when I started my system, fsck worked correctly and performed the check regulary after 26 system boots. It said something like /dev/sda3 was mount 26 times without checking, bla-bla-bla, check forced after that it showed me a progress bar and I could see the progress of checking.
Now the situation has changed. I push the ‚ÄúPower‚Äù button, the system starts, I see the boot operation sequence on the screen and sometimes when the boot process goes to the ‚ÄúChecking file systems‚Ä¶‚Äù stage the system just hang. The HDD's led is off and it doesn't blink. The system is in that state five, ten, fifteen minutes and nothing happens. I push the ‚ÄúReset‚Äù button, the system reboot and if I push the ‚ÄúEnter‚Äù key in GRUB the system boot without problems, ‚ÄúChecking file systems‚Ä¶‚Äù returns some info that I think relevant to the last successful check. But if I don't push ‚ÄúEnter‚Äù the system hangs again.
I have to notice also I performed partitions size change about month ago. I reduced the partition where the root directory was and increased the partition with the ‚Äúhome‚Äù directory. I performed this operation booting with Ubuntu live CD and using the GParted utility. Partition size changing completed without any errors or warnings.