The ICMP firewall settings in Windows Vista have been moved to a location which is almost impossible to find.

Open your windows control panel.  If you are in classic view open Administrative Tools, otherwise open System and Maintenance, then Administrative Tools.

Open Windows Firewall with Advanced Security.

Click Inbound Rules and wait.  Windows confusingly says "there are no items to show in this view" while it is populating the view.

Click New Rule.  Select Custom and then Next.  Select All Programs, then hit next.  In the Protocol type dropdown select ICMPv4 and then press next.  On the scope page leave the default values and click next.  On the Action page leave the default values and click next.  On the profile page leave the default values and click next.  Give the rule the name ICMP Ping, or something memorable to you, you can add the description that the PingCOPA network tools require this.  Then press finish.

Ping should now work fine from within the PingCOPA Network Tools.