Your problem is rooted in "split tunnels" concept.
You need to reconfigure your Cisco concentrator. It is happening like this:
1) On your corporate Cisco concentrator, the option "Tunnel Everything" is selected for the clients
2) When Cisco client is negotiating stuffs with your Cisco concentrator, it is "instructed" that it should tunnel "everything". Meaning that all name resolution requests, NetBIOS resolutions (printer/file sharing stuffs), e-v-e-r-y-t-h-i-n-g is sent through the tunnel.
3) So when your local PCs connect to the shared resources on PC (A), they won't get back any response because that shared computer is sending all responses back to the corporate network, which local PCs will never see.
Tell the corporate VPN admin to reconfigure so that tunnel/encrypt traffic only for corporate network. I.e home network is 192.168.1.0/24 and corporate is 172.16.0.0/16, then tunnel specific traffic option and specify "172.16.0.0/16". It should work.