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If you had to change the E-mail address on your Microsoft Account login as you described due to an ISP change, you would need to go to the Manage Account option once logged into your Microsoft Account on at least 1 of those 3 computers you have, and preferably using a computer that had W10 on it. HOWEVER, and this is a big however, with a Microsoft Account login which you would have to had associated with an E-mail address and password that's actively working when you setup 1 or more of your computers, this allows access to your computer as the Local Login account does as just described, but in ADDITION, you would then have complete access to the Microsoft Universe, primarily their App Store to purchase or download media content in the Microsoft Apps Store such as music, movies, and Xbox games, etc. You can still get to your W10 desktop, programs, data, and even to your Internet. The main difference is, that with a Local Login, you use whatever account you want to login to W10 with no associated E-mail address. More importantly, you need to understand the difference between a Local Login Account in W10 and a Microsoft Account Login in W10. Also, you posted your problem in the W10 forum here, does that mean that all 3 of your computers have W10 on them? Or do you have a mix of computers with different versions of windows, such as 1-W10, 1-W8.1, 1-W7? It would be helpful to know that. It's more likely that you had a problem with using different types of accounts in W10 and that's causing the issue with your MS account.
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It's unlikely you had problems this recently due to that switchover. Well, Microsoft bought Skype back in May 2011, over 5 years ago, so that's quite old news. Result - whenever I now try to use any office tool or microsoft related app, I am told to log in again. It finally closed a day or so back, and anyone now contacting it gets a message to tell them why.
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That was the end of that conversation - except that I wanted to tell him my email address linked to my account was due to close as I had transferred IT suppliers. He decided it was a network problem and rang off, saying that he was not trained to do networks. I could not fix the problem, so I rang Microsoft help line and had a long conversation with an engineer. Each time I logged on with my laptop I got a message like "fix your Microsoft account or apps will not work on your other devices". As a result, I ended up with different usernames and passwords on the three machines, some with correct details, and some with different ones. Last Monday while logging in to Skype with my usual frequently used and long held username and password, Skype refused to continue until I had entered my Microsoft account username and password. I also have a common account for Skype that worked on them all until Microsoft bought out Skype.
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