"However, what you meant in idle without doing anything. If so, then my computer will be in a sleep mode."
By idle I mean you are not running any programs, just watching screen and the core temperature to see if it drops or increases with the Windows doing nothing but displaying the desktop.
Intel processors have an internal temperature sensor and if the temperature reaches or exceeds a certain value it throttles back / down the speed, which may be what is causing some of the slow responses or stops responding.
As for replacements parts I do not know of any place were you can purchase them in Yemen. I suggestion is that you send an email to HP's US or World wide support site, they may know of a place near you.
http://www8.hp.com/us/en/contact-hp/ww_office_locs.html
Or: http://www8.hp.com/us/en/contact-hp/contact.html
Buying an old fan may help if you have some means of testing before you buy it or get your money back if the fan doesn't work.
J W Stuart: http://www.pagestart.com