Error 403 when logging into dashboard

Some users of the website I admin are getting an Error 403 when they try to log into the dashboard. The error reads

Error 403
We’re sorry, but we could not fulfill your request for/wordpress/wp-login.php on this server.
You do not have permission to access this server. Data may not be posted from offsite forms.
Your technical support key is: *4 groups of 4 letters and numbers in combination*
You can use this key to fix this problem yourself.

This started after upgrading to 2.7.
What does this mean and how do I fix it?

I’m new to wordpress and being a site admin. I’ve tried find answers by searching the forums but have not had any luck so far. Any help is appreciated.