It appears the SalesForce website does not work! If I go here (I have tried this in multiple browsers) https://help.salesforce.com/ and click Contact Support -> Open a Case, it redirects me to https://help.salesforce.com/hthome?err=1. It does this whether I am logged in or not.
This has been well documented, but apparently never fixed:
I am really surprised something so simple has slipped through the cracks.
How can I submit a support case?