To briefly recap my experience on a similar issue of being unable to connect to a wifi router from a white Macbook under Mac OS X 10.6.5, thus the internal Airport card, I've changed my WEP password to WPA on all our machines, and tried all sorts of other things, all to no avail, but as my Wifi works OK on the Windows XP-Bootcamp side of my machine and on our PowerBook G4 under Leopard, my iPod Touch 3 and my son's iPhone, the Airport card on this machine and the router are both eliminated as causes, leaving only the Mac OS X update 10.6.5 as a possible cause. Why would 10.6.5 put more demands than previous updates on the router? I use 802.11g, not n. On a Belkin Wifi/Ethernet router with the firmware kept up to date.
For more on this, see
http://discussions.apple.com/thread.jspa?messageID=12631919
BUT THEN I saw somewhere (probably on one of the Apple forums) that someone with this problem, but who had a Windows system with Bootcamp on his machine, on which his WiFi worked properly, found that after re-starting from the Bootcamp side, but in the Mac OS X side of his machine, his Wifi worked again straight away. Just as it did for me after initialising the new WPA password on it.
I have just tried this AND IT WORKS!!!
Total mystery.
I have yet to try another recipe of turning off the IPV6 in the preferences, but that recipe only worked once for the person who noted it, Todd, in
http://osxdaily.com/2009/09/01/how-i-fixed-my-dropping-wireless-airport-connecti on-problem-in-snow-leopard/
BUT then after about an hour of inactivity, I came back to my (still open and awake) machine to find the Wifi connection gone again - could the fact I had re-plugged in my Ethernet cable have anything to do with it?
I see there are a few things recommended in this forum that I have not yet tried, but not many - for example DrVenture's Ping test, and using DiskWarrior, in my experience one of the best recovery tools around.
I shall continue to look for a solution, I hear Cupertino is coming back from Christmas and New Year holidays on 3 January, and I certainly don't expect a solution from the First Aid people or the Genius bars - there's almost certainly more expertise in this forum than most of them, this is no longer about diagnostics and work-arounds on the basis of what exists, it is clearly an Apple 10.6.5 update problem that only those with access to the code and the logic behind it can solve.