Hi,
I do not know what is wrong to the CentOS, as I only get this
https://dl.dropboxusercontent.com/u/40211031/tt296.jpg

after having started it.

Well, a few more details are needed. For starters:
What version of CentOS?
Is it in a VM? If so, what are you using? (VMware, VirtualBox, qemu...)
Is this a fresh install? If so, did anything go wrong? How many times have you tried to install it? Did you do something different each time?
If it has been working but recently stopped, what changes have you made to it since you last rebooted it? Updates, or even changing a config file somewhere?
Have you ruled out a hardware issue?
How long have you waited for it at this screen, compared to how long it usually sits here?
What have you tried so far? Has that caused any change?
Have you found anything relevant in your searches?

Additionally, you should probably take a look at this.

Also, when the boot starts, have you tried selecting the "debugging" mode? If so, what happened?

Are you in a dual boot with Windows and did you modify the GRUB Menu?

Do you have the CentOS installation CD/DVD?
If so; you can use it to rescue your os and debug like frankbell has sugessted.-

Thanks all.
It is Cent OS 6.5. How to start it in Debugging mode?

Strange, I see 6.7 in your screenshot. Anyway:

At an early boot phase, it will ask you to hit any key to interrupt the boot process. Do this. You may have a menu option that indicates recovery or debug etc. Select this one.

If you don't have this menu option, type "e" to edit the grub command line, then remove rhgb and quiet from it (this is from memory, I am not sure). Type "b" to boot. This will display startup messages and show you where your system initialization is hanging.

There are instructions with screenshots on the internet, but I can't find them right now.

I press "e" and then "b" to boot, but I still get the same screenshot as shown in above and do not see the reason of the problem. Please advise.

Have you removed "rhgb" and "quiet"?

How to do these? Can I have more details? Thanks a lot

To access the Menu Entry editor press the 'e' key from the bootloader.
e is for edit
o is for insert a new line
d is for to delete a line

After pressing e for edit remove the words "rhgb" and "quiet" from your kernel line.
After the changes the 'b' key will boot the os.

If pressing 'b' for boot doesn't work hold down Ctrl and the 'x' key an your os should start.

http://serverfault.com/questions/405...ing-and-future

Sorry, I do not know what I should do next, below.

https://dl.dropboxusercontent.com/u/40211031/tt303.png

you have to take a closer look at the line that continues to the right, with a little arrow ->.
you have to do something to that line (i don't know what though), then try booting again.
research & some trial and error (read: try many times).

Follow the instructions on that screen:
Using the Arrow Down key, go down one line to the kernel line
Type e for edit
Using the Arrow Right key, scroll to the right until the end (the END key might work as well)
You should see strings "quiet" and "rhgb". Use arrow keys and Delete and/or Backspace to remove them
Type b to boot

Rather than a progress bar, you will see messages showing the initialization process. At some point, the process hangs - the messages at that point will help us understand what's wrong. At least, that's what we hope.