This worked for me FINALLY - but it's very glitchy! I posted earlier all the steps I took (like 8 different steps) but nothing worked in logging me into iTunes using two different Windows 10 computers. I kept trying different things and finally got into my account but there's obviously something wrong with iTunes from the Apple/Microsoft end that they need to fix. In the meantime, this worked for me to get into my account AND buy music after more than 24 hrs of failure:
1) logged into iTunes but instead of clicking on "sign in" after I entered my password, I hit ENTER a bunch of times (more than 10) and I was suddenly in my account. My music library appeared
again.
2) BUT the screen was frozen. I couldn't do anything, not even
X out. At this point, I went to Task Manager (ctrl+alt+del) and chose END TASK for iTunes to close it out.
3) I opened the iTunes app again and I was in my account without having to log in again. Now I could play my library music files, I could
access the store and find songs - BUT it was not allowing me to purchase anything because it wasn’t taking my password, telling me something was wrong with the server. Hitting enter a bunch of times here didn't work. But I was still in my account.
4) found a song in the store I wanted to buy so it was listed on my screen. DO NOT purchase, just make sure it’s on the screen.
5) clicked on Edit, Preferences, Devices, Reset Sync History, OK.
6) clicked on Edit, Preferences, Advanced, and then (a) reset file location, (b) reset warnings, (c) reset cache, (d) reset identifier, (d) OK
7) at this point I was able to buy the song I wanted as it accepted my password as always.
8) I tried to change my account to "never require password" to make purchases but that didn't work because it wouldn't take my password. Hitting ENTER didn't work here either.
I had to repeat steps 4 to 7 in that exact order every time I wanted to buy a song. It's a royal pain but at least I was able to access my account and buy music, too. Hope Apple and/or Windows fix this soon!