A different situation from what most people experience on here: A new Air will not connect to the Internet via our home router (though other MBs will) and the Air will connect to the Internet via other routers at other locations.
We bought my mother a new 13" MacBook Air (so: purchased May 2014). From the start, it's had issues connecting to our LAN. Other computers, including my 2011 MacBook Pro, connect fine.
I've tried multiple times running the Wireless Diagnostics and connection wizards that come with the Air, which offer no help. The Air also can connect to the router via Ethernet and gets the Internet connection, but obviously we don't want to do that all the time. My mother brought her Air to her work today and connected to that Wifi network without issue.
At home, our computers connected to the Internet run an IP address in the range of 173.195.x.x. Hers runs at 166.x.x.x whenever it doesn't connect properly, but if I renew the DHCP lease a couple times and keep switching settings randomly then I can connect the Air to the network until the Air sleeps. It's an unreliable method.
Specifically, the Air has this IP address but does not say this address is self-assigned. It also does not tell me that I 'won't be able to connect the Internet'.
My suspicion is currently with the router. It's about 3.5+ years old at this point, a Netgear WND3400 N600. I think it may just be that it's a wireless-n and the Air is wireless-ac, but the Air should be backwards-compatible.
I haven't updated the firmware on the router, I'm about to do so now.
Does anyone have any ideas for me to try out?