Ubuntu cannot load

Ubuntu only load when I click at Ubuntu, Linux 2.6.31-14-generic. Why?

Log in to ubuntu 2.6.31-14-generic.
Then in the terminal give the command :
sudo update-grub
reboot.
See what happens.

Hello, I updated the grub as Digvijay Patankar said. What happened is worse for me. Only command appears like this.

sh. grub>

that's it. And I do not know how to login my Ubuntu. Please further help.

grub> find /boot/grub/stage1
This will search for the file name `/boot/grub/stage1' and show the devices which contain the file.
Then give the command setup (hdx) where hdx is the output returned by above command.
like :
grub> setup (hd0)

This command will install GRUB on the MBR in the first drive.

Here I assume that your system has only single HDD and only one OS which is Ubuntu.

at the
sh: grub>

I typed as given:
sh: grub> find /boot/grub/stage 1

But error occured. Command not recognised. There no such command find

I have 2 partitions, and 2 OS (Ubuntu and Vista)

well, you need to provide the output of following command :
sudo fdisk -l

You mean '2 partitions' or '2 Hard Disks'?
if '2 partitions' then you dont need to worry about the first command.
simply give the second command. and then quit
reboot.

I have 2 partitions C: and D: in single hard disk.

At the beginning, it appears
sh: grub>
instead of grub to choose from.

As instructed, I typed like this:
find /boot/grub/stage1
and the result:
error: unknown command 'find'

So I proceeded with the second command at
sh: grub>
I typed
setup (hd0)
and the result:
error: unknown command 'setup'

Thus, I cannot login into my Ubuntu, after the upgrade.

Use LiveCD and download 'Super Grub Disk'. This will solve your problem in an easy way.
Burn the iso image to a CD and boot it with. It will install the GRUB2 with whatever required.

Where is the option of 'Super Grub Disk'? There is just an option of Ubuntu, and memtest. The machine in use in, HP Pavillion DV6 Notebook.

Have a look at https://help.ubuntu.com/community/Grub2#Reinstalling%20GRUB2 to reinstall Grub2.
Check that in /boot you have kernel and initrd of 2.6.31-16-generic
2.6.31 is old, which version of Ubuntu are you using ?