I was getting the same "too many attempts" "check later" and "we will send an email to you for a new password" when attempting to login from my computer, but both my mobile devices have no problem logging in - all both the current User and same Password. After spending a few hours trying multiple different approaches, I noted that the user on my chrome browser had changed from XXXX@gmail or XXX@yahoo to just XXX,
I then closed the browser, reopened it (same Chrome browser) and logged into my Yahoo account, The user -top right - then became my usual yahoo user. I then opened my Dropbox account which uses that very Yahoo account name, and now the password that my phones etc use also works on my browser. This of course had little to do with messages I receiving from Dropbox, but it appears to be that (given my limited browser knowledge) it is situation where the browser needs to show that the browser user needs to the same user that Dropbox uses. (so I guess, but I never saw this info in the documentation, in the help window, or in various discussions)