Hmmm, I'm wondering why Netios over tcpip is disabled in your second adaptor, still I should think you would be able to get an IP. My personal favorite of little dsl routers is a Linksys with 4port switch built in. They've proven cheap and reliable and easy to configure.
NetBIOS over TCP/IP wouldn't affect this. If you've turned on ICS, it appears that some kind of firewall might be blocking DHCP requests from going out. Either that, or you've not set the client machine to automatically get an IP from the machine doing the routing.
...But I agree with bentkey: Get a hardware router, like a Linksys. It will save you tons of headaches.