Can't ping both ways

I have two computers, both running XP Pro, connected with a crossover cat45 cable. Computer A has two nic's, one connected to cable internet, the other connected to Computer B.
Computer B can ping Computer A and can access the net through A's connection. It can net view A's resources using its (manually set) ip address but not using its "name". But it can't see A through "view workgroup computers". Network places and the printer on A can be accessed by B by adding network places using the ip address
Computer A can't ping B (manually set up ip) and can't be "forced" to access its resources although it can see B through "view workgroup computers
B has no firewall enabled; A has a firewall on the internet nic. Both A and B have their resources shared on the network
B was recently purchased new with XP preinstalled. Is it possible that B has been configured with security preventing external access? Where do I look and what do I look for