Since El Capitan, I cannot log in to ANY THING iCloud on my 2011 MBP. Please help me.

I have no idea what to do now. I can access my iCloud account via the website, and anything else for that matter that needs 2-step verification.

I must maintain a very high level of security on my machine, and I have 2-step turned on.

Here's what happens when I try to log in to anything iCloud on my MBP:

And it sits, sits, sits.

I've not been able to login to iTunes, iMessage (that one has been since Mavericks, funny enough, so iMessage on my machine has been completely unusable), iCloud Drive, none of it.

I've tried this, but I can't access it because I can't even get iCloud to do anything:

https://www.reddit.com/r/apple/comments/3ndlb4/since_updating_to_el_capitan_i_ge t_this_pop_up/

Tried this:

Check your Apple Music library settings - Apple Support

This:

https://www.reddit.com/r/applehelp/comments/3nglyc/your_icloud_session_has_expir ed_popup_is_*******/

I'm stuck. I have everything integrated. Whenever I try to log in to something via a browser, the 2-step works great. Does anyone think this is related to that, and El Capitan? El Capitan is really making me regret El Capitan-ing.

Thanks everyone.

JimOnLight