Snow Leopard: can't log into App Store or download El Cap

I am running a clean install of Snow Leopard (10.6.8) on a 2009 Mac Pro. I want to upgrade to El Capitan. I am unable to log into the App Store to see my prior purchases; the Purchases list tells me to sign in, but nothing happens when I click the provided link. The Upgrade button for El Capitan in the Updates list doesn't work. (Neither does the one for Mountain Lion, which is the only other thing in the Updates list.)

Accessing the El Cap download page (special version for Snow Leopard) from an Apple Support page (How to upgrade to OS X El Capitan - Apple Support) works, but nothing happens when I click the Get button.

How do I correct these problems?