Keep getting email saying authenticate or you will lose your email account!!

About a month ago I started getting this email:

Windows Live Account Authentication:    

Dear Hotmail Account User,       
• This message is from Hotmail Customer care messaging center, to all Hotmail account owners. We are currently upgrading our data base servers, and e-mail account center.
  We are deleting all unused Hotmail accounts to create more space for new accounts. You will have to Authenticate your Hotmail Account below to show you are human and to prevent a permanent closure of this email address.
  Do not click on external links, authentication should be done using the authenticate button below. Successfully authenticated addresses will be automatically notified via inbox.        
• Click here to Authenticate
• When I click authenticate, I get an error that says it is a bad site, so I cant authenticate. I replied twice and I was sent a message that "Its a scam, I got hacked" I don't want to lose my email account so I need to know for sure. IS THE EMAIL A SCAM???