It is not possible to ping your windows vista computer from another computer while having your firewall enabled. Yes the most simplest and the most drastic solution is to disable the firewall. But there are better ways to get over it.
Enable ICMP Echo Request
Open an Administrative command prompt. This could be done by right clicking the cmd --> Run as Administrator OR in the search pain type cmd and Ctrl+Shift+Enter
Once you open it type the following to Enable ICMP Echo Request
netsh firewall set icmpsetting 8 enable
To disable ICMP Echo Request
netsh firewall set icmpsetting 8 disable
Hope this helped most of you out there wondering how to enable a ping request on your Windows Vista PC without having to disable the firewall