No offence and all, but I do wish people wouldn't keep recommending static IP addresses as a 'fix', it causes me no end of headaches when it bleeds onto corporate networks and I've got to spend half the afternoon trying to find it.
Stuff like this is hard to diagnose without being in front of the machine, WiFi can be a complete pain. I'd look to disabling WPA temporarily as a diagnostic step (one less thing to worry about) and I'd question the assumption that "they're both the same" when it's immediately followed up by "apart from these differences". Is one b/g/n and the other b/g only, perhaps?
Are they using Windows to manage the connection, or some proprietary OEM software?
Can you get the laptop to connect to any other wireless networks? Ie, is the problem "it won't talk to this router" or is it "wireless is broken"?