GRRR!! GRRR! DOUBLE RUDDY DOUBLE GRRR!
No, I'm not getting annoyed at you! It's flamin' Microsoft that annoys me by giving the same name to two entirely different things!!!! (There have been loads of thread on AB where the confusion between Outlook and Outlook.com has led to misunderstandings).
It could be that your IP address has become associated with spam, resulting in it being blocked from sending new messages. (Most ISPs use 'dynamic' email addresses, so you could currently have one which was previously used by a spammer). Check your current IP address here:
http://whatismyipaddress.com/
Then disconnect your router from your phone line (/cable) and wait a minute or two before reconnecting it. Go to the same link and check that yoo've been allocated a new IP address. Then try sending mail again.
Also take a look here to see if anything is relevant:
http://windows.microsoft.com/en-gb/windows/outlook/errors-sending-mail
If not, try the 'Contact Customer Support' link at the bottom of the page.
However Hotmail/Outlook has always been an abominable service. If you really get stuck (or you're simply wise enough to seek a better email provider anyway) get a new email account here
http://www.gmx.co.uk
and use the 'Mail Collector' facility to get emails sent to your old Outlook address automatically forwarded to your new GMX one.