Dual-band Extreme ignores certain devices

Pulling my hair out on this one.

Have one of the dual band Extreme models; it's a couple years old, got it shortly after they came out.

It's running firmware 7.5.2. I realize there are newer versions but they caused more trouble than they were worth, so I rolled back.

After a hard and factory reset, many modem powercycles, and restarting devices and double-checking configurations, ... everything looks right, yet there is a MacBook Pro on the network that does not get Internet connectivity. It used to work just fine before; the connection uptime was insanely good and throughput was fantastic as well. There wasn't really any trigger event, it just ... started one day.

It's got me completely baffled that it can get onto the network, both via Ethernet and Wi-Fi, but it won't go online; I can ping it and share files and even ssh into it but it can't get internet access. I ran the AHT on it and it checked out. It was able to get online just fine with another open wifi network in the area (belonging to a neighbor.) We have a bunch of other devices like a Wii, a couple older TiVos, four iPhones, four other Macs, and a Windows machine, and they are all having no trouble.

Occasionally one of the other devices will not have a connection for several minutes after waking from sleep or booting (or otherwise making a connection attempt to the Extreme,) but eventually they'll connect and be fine for days. I don't know if this is related.

The logs in AirPort Utility 5.6 have been useless. The light is solid green, everything is set up right. Modem -> AirPort Extreme -> devices. MAC filtering is off.

Really hoping it's not the router hardware going bad. These things are not cheap and it's definitely out of warranty by now.