My PC can connect to the internet, seems to have no problem, except sometimes I lose the connection in the middle of browsing.
The question that I want to ask anyone here is that why my PC gives the result of "request time out" when I ping the sites that I can log on/assess quite well? For example 'ping' results in request time out, but I can assess that particular site well.

Any idea about what's happening?

the server simply doesn't allow incoming ICMP. quite a common practice

ICMP is the protocol the ping command uses