Kindle Direct help number?

The contact us section is an email form, rather than a list of phone numbers. What error are you getting when you try to sign in? It might be someone's had that issue and knows what to do.

My log in process with them changed about a month ago. I log in with user name and password and then get a page that has the sign in button on the top right and I have to click on that link to actually get into my account. But sounds like what's happening to you is different.

Have you tried a different browser type? I use Mozilla whenever I have a weird log-in issue on a site. (My default is IE because I'm weird.) Usually it's a pop-up that I'm not seeing or some weird something or other that needs to run and my IE settings won't allow it.

You should be able to have them call you. I don't think there is a number you can call though.

If clearing your cache and other browsers doesn't help, trying a computer at another location might (sometimes it's because of something like your virus software is over-zealous or your network has blocked those pages).

If it's definitely the account rather than anything else, you could sign up a temporary account and use that to contact them.