Upgraded two of my machines to Windows 10 yesterday, and have been unable to connect to either one remotely via Logmein since. I get a "login failed" message with a reconnect button (which, when clicked produces the same login failed message), and a close button.
I also trieed to share a desktop and sent myelf the link, but even that produces the same "login failed" message.
And yes, I have installed the optional Windows 10 update on both machines, and I've rebooted.
Oddly enough, while logmein doesn't, Join.me DOES work.