Your LiveID does not have to be a valid email address. Mine has never been, and I've used it successfully for over a decade (before it was even called LiveID). You can associate a valid email address with your account in My Settings (for alerts),
but that is a separate issue.
This forum doesn't cover Live ID issues. You can make a request
via this form.
Or report the issue to the
WL Forum. Or request support here
Support page.
Richard Mueller - MVP Directory Services