Ping icmp echo

Hi I'm a newby

Had a laptop for 5 years did the basics - surfed the web, bought items online and never too ambitious. Always security concious - or is it paranoid - so I periodically checked with GRC to re-assure me that my laptop was not vulnerable to hackers. If that's possible. Always came away happy that no ports were accessed and my laptop ignored pings. Now I have a new laptop which has the ports ok but failed by acknowledging a ping test. Any solutions for a thicko to do basic and I mean basic tweaks.

Thanks guys and gals in advance

 

Hi

"After installation, test the FW and all ports which are both closed, stealth or listening using Sheilds-Up."

It was after using Shields Up that they failed my laptop for answering the "ping".
Previously I used Windows own firewall, but getting a better laptop I though I should get "upmarket" and installed Zonealarm Pro. Now I get the fail on an answered "ping" with Zonealarm. Is there anywhere to tweak ZA to make the ping unanswered or is there always a need to answer the "ping" but not allow access to any ports - which were 100% secure.
Thanks again