Having problems with losing internet connection after 30 min or more online.

While searching on the internet I get the message that I am "not connected to the internet". To correct this I restart the computer. I had this problem before and ran the Dell diagnostic program. While this was happening the internal fan could not be heard running. I tried to find a way to test the fan but could not find anything. Once again this is happening and again I can not hear the fan running. Is there any way to test the fan before tearing apart the computer This is an Inspiron 1545 running windows 7. Any help will be greatly appreciated.