I knew LinkedIn was a giant piece of shit, so this just confirmed it. You get locked out if you don't verify identity in a certain period of time. A smart phone and app is required in order to upload verification data (government id and a selfie). You cannot contact support unless to can sign in.

So to recap, I cannot access, edit, or delete my account without sign in, I cannot sign in unless I verify my identity, I cannot verify my identity without a smart phone and their fucking app, I cannot contact support to help me without access.

This is by design. Instagram and Snapchat also require the app to be installed on a smart phone before web access can be temporarily authorized.