Thanks for your replies. What I mean is that is the only address it ever shows, both under Apple System Profiler and the TCP/IP control panel.
When I go into the TCP/IP control panel, and I click on Connect via, the only ethernet option is the built-in one, which doesn't work. There are AppleTalk (MacIP), Ethernet built-in, and PPP.
When I go into Apple System Profiler, and when I click on Devices and Volumes, and then click on the PCI slot the network card is in, it shows something there. The info it gives there is:
PCI Slot
Card type: Not available
Card name: pci10ec,8139
Card model: -1
Card ROM #: Not available
Card revision: 16
Card vendor ID: 10EC
I looked up the vendor ID and 8139 and it is RTL-8139/8139C/8139C+ Ethernet Controller manufactured by Realtek Semiconductor Co., Ltd. I found the driver for Mac OS, but it was for Mac OS 8. The extension is listed under Extensions in Apple System Profiler, and it says it's enabled.
Under TCP/IP, if I set the Ethernet built-in to Auto DHCP, it always shows the 169.254 address. I have it connected to the physical ethernet 4-port switch on my wireless router. I can't ping it from my other computer that is working on the LAN.
I have no idea how to make it use the network card in the PCI slot instead of trying to keep using the bad built-in ethernet adapter.