If you are using encryption on the linksys, make sure that the encryption setting match on both sides, for example if the linksys is configured for 128 bit WEP, make sure the airport is configured to use 128 bit WEP.
Hopefully that might help. That being said, here is my two cents on wireless. I cut and pasted this from another reply I wrote for someone else, It refers to airport, not airport extreme, but both can support WPA, If you are already running Panther you can ignore the Jaguar vs Panther stuff too, put I'll leave it in here for anyone else reading this, because any airport on Jaguar can not currently support WPA, which is much much more secure then WEP. By the way, in addition to the stuff mentioned below, to further secure my wireless, I only use the wireless access point as a bridge, and do not allow mine to run DHCP, so I have to configure TCP/IP setting manually. Just an additional step to prevent people from hopping into my network.
Here is the pasted text.
Both the Linksys WAP device you have and the Airport running on Jaguar will only support 128 bit WEP as the maximum encryption. As I work with security, I personally do not find this exceptable, because of inherent weaknesses in WEP. It will obviously have cost associated with this recomendation, so you will have to determine if a secure network is worth the cost or not.
I would recommend buying a wireless access point that supports WPA. Then configure the WAP device to use WPA for security, run as a closed networked, and allow only the MAC (Media Access Control) address of the Airport on the Macintosh to join the wireless network. However to use WPA security on the Macintosh, you will need to update the Airport software to at least version 3.3, and to do this you will have to be running Panther. As I said there would be a cost involved, but for me, I would do whatever I could to stop someone from accessing my internal network.
Cost here ... let's see
[Edit] Went to linksys site to verify info, They do say that they have added support for WPA, so you may be able to flash the firmware on your linksys if it does not already support WPA. I would recommend using WPA. For WPA in the Macintosh, you can go to Airport help and search for WPA. [end Edit]
Buy a WAP device that support WPA, such as Airport Extreme Base Station.
Upgrade the operating system on the Macintosh to Panther.
Anyway good luck.
Some additional reading about WEP (an older doc, but just lets you know how long the problem has been around.
http://www.sans.org/rr/papers/68/149.pdf
Good document on caomparing WEP and WPA, plus securing wireless in general
http://www.giac.org/practical/GSEC/Stanley_Wong_GSEC.pdf