Any good firewall will have a "stealth" mode whereby incoming pings are simply ignored. This will make it look to the person pinging you as if you do not exist, their pings will just time out.
that isn't strictly true, and whilst it is up to you what you do with your machine I'd like to point out that not all network traffic flagged up by personal firewalls is malicious, although you could certainly make a case that it is increasingly likely.
There is no guarenteed way of securing a network short of unplugging it and whilst a firewall will help it is only a way of reducing the options for someone attacking you. It is no protection against an unpatched computer, especially one which you want to use in any meaningfull way (that is to say any network is only as secure as the services you expose on it.
in 99% of cases "attacks" are indescriminate and essentially untargetted, a good firewall and a suitably patched network on the back end of it will mitigate the vast number of these attacks. However, if someone deliberately targets "you" then it's a great deal harder to keep them out :(
Then again, the majority of "attacks" at the moment are people emailing viruses and/or sending emails which say "hello, this is paypal, can we please have all your credit card details", which you wouldn't have thought would be that hard to spot :)
