Safe bet he's using ICS.
OK, you got it working with a static IP but DNS didn't work. That's because you didn't configure the DNS servers, which, as Jman said, can be entered in redhat-config-network on the DNS tab.
The values you want to enter can be found on the Win 98 box by...
Start Menu -> Run
Type in "winipcfg" and press enter.
That program will contain at least 1 DNS server, likely 2 servers. Copy them (preferably in order) to the Linux machine.
You can else enter them manually into:
with the syntax: