|"I am trying to run it through my serial port. I have a |
serial to ethernet adapter"
I don't believe that will work and that is the source of your problem.
You need a old pcmcia card that is a nic. Most likely the only thing you may find of that vintage is a combo card like a Xircom.
Might try ebay for that.
BTW since wfw has no updates/no firewall/no protection your laptop is at great risk when you do finally get on the internet.