I am trying install Windows 8.1. It is in the "Checking compatibility" for more than an hour. the progress indicator reached "b" in word "compatibility" and does not move forward after this for long time.

Pauses may suggest an issue. The issue could vary from bad hard drive sectors to corrupt installation. To check if your hard drive is good you may boot with the installation USB/CD and use the advanced recovery options and open up Command Prompt. Through there you can use check disk tool to make sure your hard drive is not the issue.
If it's fine you may format you USB drive if your installing from USB.
If you are installing from DVD you should re-burn it.

If this is the official installation from the Windows Store this may open up to other possible issues. 

Hi,

For the issue, I would like to know how do install windows 8.1? Windows store? or Windows 8.1 media?

I suggest we use clean boot mode to narrow down the issue.

How to perform a clean boot to troubleshoot a problem in Windows 8.1, Windows 8, Windows 7, or Windows Vista

http://support.microsoft.com/kb/929135

If the issue persists, please check the event view to see if we can find the error log in the event view.

Regards,

make sure that all the drivers are updated,

uninstall any third party software ,

temporary disable antivirus or security prog..

perform a clean boot

please have this question marked and closed if it's solved. Thank you