I know a lot of posts have been written, and I had read most of them when I encountered the problem. None of them solved the problem.

I have successfully installed Ubuntu 12.04 on top of Windows 8. Now my PC simply boots into Windows 8.

If I press 'Esc' at start of BIOS, and then F9,the GRUB shows up and Ubuntu is listed at the top of the several options to boot from.

I did run Boot-Repair once I logged into Ubuntu explicitly from GRUB as mentioned above. I did all said by Stormvirux in this link but was still unsuccessful.

The debug info is listed here.

Something which confuses me is the message which Boot-Repair stated after it did its job.

You can now reboot your computer. Please do not forget to make your BIOS boot on sda (8004MB) disk! The boot files of [The OS now in use - Ubuntu 12.04.2 LTS] are far from the start of the disk. Your BIOS may not detect them. You may want to retry after creating a /boot partition (EXT4, >200MB, start of the disk). This can be performed via tools such as gParted. Then select this partition via the [Separate /boot partition:] option of [Boot Repair]. (https://help.ubuntu.com/community/BootPartition)

I don't know why it says it is far from the start of the disk as I see it first in the GRUB menu which comes up at startup.

One more input, when I try to place the GRUB in sda, Boot-Repair does not progress giving me the following error:

GPT detected. Please create a BIOS-Boot partition (>1MB, unformatted filesystem, bios_grub flag).   
This can be performed via tools such as Gparted. Then try again.
Alternatively, you can retry after activating the [Separate /boot/efi partition:] option.

I had to select Separate /boot/efi partition: sdb2