I'm not sure that what you're trying to do will work because Win98 doesn't have enough routing capability to determine whether a packet needs to go out the ADP NIC or the SOHO NIC. To accomplish this, you probably need to upgrade to NT Workstationor W2K Professional but I don't know if even that would work.
A couple of bits more information would be useful. Where does the SOHO NIC get it's address? Is it static or is it supplied via DHCP by the Linksys router? When you do an IPCONFIG /ALL, what does it tell you about the IP, subnet mask and gateway of each interface?
But I'm thinking that this is only going to work with some sort of routing software. What I think is happening is that your gateway address is the ADP NIC so whenyou ping the Internet, it goes that way rather than towards the Linksys router.
You might be able to accomplish this with the Internet Connection Sharing that comes with Win98SE but I would need to know more about the ADP connection to be able tomake that judgement.
The other issue is whether ADP is okay with having their network attached to the Internet by means of an unprotected workstation. That might actually turn out to be the bigger problem than the routing issue.
paul