I'll admit it - I screwed up. I network-activated W3TC and my entire network went down with a 500 server error. I had to delete the plugin and edit .htaccess to get the network back up.
Now I know not to do that. So I downloaded and installed W3TC again, did NOT network activate it, and went to one of the blogs to activate it. Unfortunately, it isn't showing up in the list of plugins I can activate!
I'm sure this problem is just some leftover from my initial clumsy attempt to fix the first problem I caused. Any suggestions?