wireless connection (w\authentication) doesn't work, while wiredconnection does, on select laptops

Here's the problem:
Two laptops, out of 8 machines tried, cannot connect to certain sites
(yahoo mail, VPN, *some* other sites that require authentication;
gmail works). Router is a linksys WRT54-G (don't know which version,
but I don't believe it's V8). The OSes are XP Media Center Edition
(SP3) and XP (not sure which level). The Laptops that don't work are
a Lenovo T61 and an HP Pavilion dv6000. The machines that work are a
Lenovo T60p, 3 MacBooks, a Dell tower, and a new Dell laptop.

The problem laptops work just fine when connected directly with an
ethernet cable. The router has stock firmware (don't know which
versoin and I haven't tried updating it, yet), and no special wireless
settings (and there really isn't much to customize in the wireless
panels).

And, the problem laptops work on other wireless networks. Also, they
both used to work on this network, but stopped working, and haven't
worked since. (These are family members who have visited at different
times)

I am about to try a new router, but would like to try to understand
what is going on here.

Ideas?

Thanks,
Ed