I came across this issue at a customers site. We were deploying Office 365 Business as part of an MDT task sequence. Once deployed, the end user would activate the suite using their business email address.
Issue: Unfortunately the Sign In dialog box would freeze. The option to push Next would not function. Additionally the text in the box would not automatically disappear.
I logged a ticket trough the Office 365 Portal. After a couple of options we found the solution.
Solution: Reset Internet Explorer 11. Turns out the Sign In dialog box is a HTA. Give IE a reset and then we are good to go. A big thank you to the Office 365 team.