Well, it is just a guess but you could try "modprobe ne2k-pci" to load the PCI NE2000 driver generic driver. Use "cat /proc/net/dev" to see if you have another eth interface available.
For the list of available driver modules view the directory /lib/modules/2.4.20/kernel/drivers/net and there is also a pcmcia directory below that.
Other modules that are popular common interfaces are 8139cp, 8139too, tulip, and natsemi. Perhaps one of them will work.
I suppose the PCI card is also a pcmcia interface adapter that could really hold anything. So you might want to make sure the pcmcia services are loaded. This is usually done through the /etc/rc.d/rc.pcmcia script if enabled.
I think you also mentioned wireless, there is a directory for wireless modules as well under the drivers/net tree you want to review and attempt to load. If none of them work then it may be that the card does not have Linux support. But you can do a search on http://www.google.com/linux
and use the model number of the PCMCIA lan card and see if any info is reported on the driver availablility and/or usage.