So after I followed your last advice (which you mailed me personally) and after the full re-install of GRUB using 'ppa:bean123ch/burg' packages and then on the HDD in the way you explained aforesaid ('grub-install --alt /dev/sda'), let me tell you the good news that on my HP NX9420 rh450ea the bug is solved now! :)))))))
@bean:
So after I followed your last advice (which you mailed me personally) and after the full re-install of GRUB using 'ppa:bean123ch/ burg' packages and then on the HDD in the way you explained aforesaid ('grub-install --alt /dev/sda'), let me tell you the good news that on my HP NX9420 rh450ea the bug is solved now! :)))))))