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Thank you for your reply. To try to use Safari is an obvious suggestion, but I do not have it installed on the PC. On the iPhone it is possible to login to icloud.com without any difficulty with Safari. The settings page is shown with all items activated. On the iPad, the log in fails and the little whirling fan continues indefinitely, well for at least ten minutes....
I had cleared, apart from history, all of the cache in Chrome for the previous test.
Curiously, trying this on a Linux machine (running Cinnamon-Mint) and using Firefox iCloud does not display the dialogue, but there is an outline on a blank screen of about the correct size, but without content. Refreshing the page takes me to the Settings page exactly as shown in the previous note. Trying to access 'Veriy my identity' takes me to the sign in screen and from thence to the blank page with the empty outline of a dialogue. So the behaviour in Firefox under Linux is quite similar to the behaviour in Chrome under Windows, expect that one cannot see what is on the dialogue.
I have tried on Microsoft Edge and Internet Explorer. Microsoft Edge displays similar behaviour to Chrome.
Internet Explorer 11, with its default settings, complains bitterly (and badly) under Windows 8: "This page canrsquo;t be displayed
Turn on TLS 1.0, TLS 1.1 and TLS 1.2 in Advanced settings and try connecting to https://www.icloud.com again. If this error persists, it is possible that this site uses an unsupported protocol or cipher suite such as RC4 (link for the details), which is not considered secure. Please contact your site administrator. " I think someone forgot to insert an ampersand, and someone else did not do the QA very well. Also whatever code was used to generate the message had failed to interrogate settings correctly as TLS 1.0, 1.1 and 1.2 were already turned on. Now is this Microsoft code in the browser - perhaps not as surely the browser can correctly interrogate its own settings - or was it Apple code in the icloud.com default page. Given the problem with the uncertain and impossibly demanding dialogue, I do wonder whether it is Apple code that is failing in all of Firefox (under Linux) and IE (under windows 8) and Chrome (under Windows 7, 8 and 10).
Under Windows 10 IE11 also complains, again badly: Unsupported Browser You can use your current browser, but iCloud works best with the latest version of Safari, Chrome, Firefox, Microsoft Edge, or Internet Explorer. Given that the machine is set to apply updates automatically, I think it is running the latest version of IE11. It then complains the there is a connectin error: iCloud encountered an error while trying to connect to the server. Well it had no problem connecting with Chrome and has no problem connecting with Apple. The support option on the message takes me to support.apple.com which confirms that all services are operating normally, but fails to provide a scroll bar to allow one to read down to the bottom of the page.
Perhaps it is a bug in the Apple code on the default iCloud page which is causing the problem in all but Safari. I am sorry that I cannot presently test on Safari.
Perhaps I should have mentioned that on the Windows 7 machine, I have the iCloud desktop app installed. This runs quite happily, and displays the details that I would expect to see on the iCloud settings page.
I have provided more information, but sadly not the specific piece that you wanted. Have you tried Firefox, Edge, IE or Chrome?
Kind regards