Hi Markb56,
When you say "Office365 rejects my login ID and Password", could you provide the detailed error message you received?
And if you can log in to OWA using IE10, it proves that your Office 365 account works well and this issue relates to the browser.
If the error message is "Cannot use this ID to access this service. Please sign-in with a different ID", please refer to this link: http://support.microsoft.com/kb/2555521
Thanks,
Bourne Zhang