I just had to work on a 98se (second edition) OS for a friend and installed a
3com 3c905c-tx PCI network card on the machine and had the same problems
described here. This is what I did and everything worked fine.

I installed the NIC card and drivers.

I uninstalled all network protocals:

IPX/IP
TCP/IP
Networks for Microsoft

etc

I rebooted the machine and windows 98se automatically recognized the NIC
card and previously installed drivers then automatically reinstalled the
PROTOCOLS for networks.

I connected my RJ-45 cord to the NIC card and then:

I clicked Internet Explorer and was online.