The article https://support.apple.com/en-us/ht2594 contains information about the requirements for a connection to a base station with WPA security (if this is what you are using). However, although a plain AirPort card (802.11b) is mentioned there, it appears to be unclear whether it in fact is possible to use such a card with WPA. You may want to study posts in the AirPort communities to begin with.
You may also (temporarily) want to switch off encryption (or use WEP) at an available base station (router) for a test. If one can connect then, you know that the problem is related to security settings.
One alternative could possibly be to use a USB wireless adapter (with WPA/WPA2 capabilities), but these do usually require at least Mac OS X 10.3 (often higher). So, make sure that driver software is available for your system before you buy.
Another option (albeit less portable) could be to connect a wireless Ethernet bridge (such as Netgear WNCE2001 or Linksys WET610n) to the Ethernet port. This kind of adapter does not need special drivers, and can thus be used under almost any operating system.
Jan