MBP works fine but not visible on network

I have a strange problem, that for the life of me I can't seem to resolve. I'm hardly a newbie to this type of stuff, which is making the lack of success even more frustrating/embarrassing :)

I have a pretty much pure-Apple setup: two AirportExtreme routers (one acting as a range extender for the first), two MacbookPros, two iPhones, iPad etc. Love my toys.

However my one MBP does not seem to be visible from the network. I can ping anything from anything else, with the exception of this one MBP. The machine is of course connected and working fine. It can also ping everything on the network.

I've used a static IP so that I can be sure I'm pinging the right machine. I've also checked that the firewall is (Preferences -> Security -> Firewall) turned off.

What else do I need to check to diagnose this?

So, Broken MBP can ping anywhere, including other machines in your network, but can it ping itself? (You have to read that with the "Will it Blend?" sound)

The rest of the machines can ping each other, but not the Broken MBP.

Am I correct?

Does this only happen via Wi-Fi? Have you tried using a Cable?

What happens if you turn ON the firewall and make sure that in "Advanced" the machine is not in Stealth Mode:

(Security -> Firewall -> Advanced)

Looks like this is some restrictions on Wi-Fi services in OS X. I have hade the same problem but when I used cable ethernet connection - all went OK.