Hey there - have you sorted out?
I might help you to proceed, if you still need it.
Essentially, I would second for getting rid of ipv6 firsthand: came over your post while trying to recall procedure to disabling it myself, as it well helped me before, and after yesterdays kernel update I have to review setup of additional modules for my madwifi wireless driver, which shows interface with ipv6 and tries to get trough with it (not sure it equally tries for ip). That´s where dual boot helps ;-)
As to your problem, you should ensure your desktop and laptop both are going to participate on the same subnetwork, i.e. something like 192.168.0.x - you can assign addresses manually, or better set DHCP range of addresses (pick some high end interval like 200-250), but not forget, that wireless is passing walls etc., so later think again about security aspect. Make sure both computers are set to ackquire dynamic address (dhcp). If you are able to ping, but not get trough with internet names - this should be DNS issue, and you either have to configure AP DHCP to inform about proper DNS servers your DHCP clients, or stuff both computers with DNS of your ISP. AP itself better be configured with static IP, that can get to your modem, though in theory, DHCP client part of it also should grab address, but occasionally I hear clients NOT being possible to grab address from otherwise working network with some AP device.
As to linux/windows compatibility: TCP/IP level should be absolutely independent to OS, just have driver for your wireless clients. If AP has web configuration interface - it can be both used AND tuned from wherever.
Let me know, if you need further help and your situation, or post here your findings, as other people might also be poking how your case was set.