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Maybe Google didn't anticipate such a big response to Adsense, and doesn't quite have the capacity to keep up? Hopefully, they're working on adding more power to the system.
It's pretty surprising, really. I've always considered Google to be extremely stable, but the last few weeks I've had to reevaluate that stance a bit.
Apparently, something I installed changed the advanced config of IE 6.0, unchecking the box under Security: "Use TLS 1.0"
When I rechecked this, I could access the AdSense page.
And no, it wasn't a fluke. I tried unchecking it again, and voila, I was no longer able to access Adsense.
Weird. I don't even know what TLS 1.0 is, but I guess it's important :D