Can't connect to iTunes, security certificate errors, can't update iOS or iTunes

When I open iTunes, I get several security certificate errors -- clicking either cancel or continue doesn't help -- they just keep coming. I've read online that I need to update my iTunes and operating system (which I do), but I can't do either of those without iTunes. On the rare chances that I do get past the certificate error messages, iTunes says it can't connect to the internet when I try to check for updates.

I've tried checking my system date and time. I have also tried going to Keychain access and repairing keychain stuff.