Update:
I removed the NIC card and replaced it with a slightly different model (Netgear FA310TX, replaced with a FA311) and updated the driver to match. No luck, that was three days ago.

Just a few minutes ago, it popped up the "Critical system updates" dialogue box. Sure as shit, it is connecting now. That was completely random, I hate this computer. This is just like the time a few months ago it just wouldn't turn on... a few weeks and a power surge later, it fires right up.

I swear this computer can think on it's own and just goes on vacation sometimes. :doh: