Can ping outwards but doesn't respond to pings

I've got a home network of 4 PC's, I've got one machine
that can access the Internet through a router, can ping
all others (and itself) on the network but cannot be
pinged by other computers. The same goes for file
sharing (the real issue at hand). I thought it may be a
network card problem, just replaced it with a brand new
one and the problem still persists.

Any help would be greatly appreciated.