Sometimes, when you have two interfaces connected,
(in your case ethernet and dial-up - ppp)
you'll end up with two default routes which can cause
a lot of confusion for the routing of your internet packages.
This could be your problem, since it works ok if you unplug the ethernet -- which likely brings down the interface and cancels it's default route.
The w98 may override the ethernet default route once the
dial-up is established, but Linux will let you have as many
default routes as you want.
A quick check would be, from a root console, "route -n".
If there are two routes to 0.0.0.0, then delete the one
going to the router (192.168.1.1)
"route del default gw 192.168.1.1"
and try to ping an internet address (like: www.yahoo.com
If it works, then that was the problem.
Configure the router to not pass a default router
parameter to clients and it should still work for the
w98 side too.