Have you changed the Connection Settings to use the LAN connection instead of defaulting to the dial-up settings?
Open IE, go to TOOLS > INTERNET OPTIONS > CONNECTIONS and change dial-up settings to "Never dial a connection".
Yeah I got all that easy stuff chcked out. The settings are fine because under a Windows XP Pro SP2 machine the internet is ok. And Automatically detect settings did not effect my connection problem. Never dial a connection is of course on. I'm going to try a Proxy server.
You can use some routing software like WinRoute.
You could also run winipcfg to see if the Win98 box is picking up an ip address from the router.
As you are able to ping an outside website, then the problem is within IE. Check your connection settings again. Perhaps you have a proxy server from before, and IE is still using it. IE under Win98 is always troublesome. it might be an idea to install firefox or something like it, just to get away from the prob.
If you can ping google.com then the routing is fine. The problem must be with the connection settings in IE. Make sure you have no proxy set, unless your ISP requires one. Also, make sure if you are using a personal firewall, like ZoneAlarm, that it is not blocking IE.