You should consider again, which services will e-smith server provide to your lan and wich ones will be provided by win2k server; you are losing internet connection because there could be a problem with the DNS server or the gateway IP routing of your lan.
I still dont understand something, If your only gateway to internet is the e-smith box, then why you need dns service for your lan?
you are using both: wins name resolution and DNS resolution, and that can be confusing (in your case in fact it is)
Win2k keeped wins resolution just for backward compatibility but with the release of win2k is obvious that the goal is replace wins and netbios names with DNS and host names/IP address.
If you have many clients or servers running win NT 3.51 or win 3.11 you will still need wins If that is your scenario you can still use dns service of e-smith and wins service from WIN server
you will have to change lan configuration of tcp/ip protocol on each client to reach dns service and gateway at e-smith's internal NIC IP address.
In my opinion (not remotely an expert, of course) thats why you are loosing connection, you can ping internally cause you are on the same network segment asigned by your dhcp but your dns server (win) is not working as expected.
e-smith has an excellent dns server, and you can still use both but you will probably notice a little perfomance decrease and more configuration time per client.
Hope this help