OK, I am thinking you are seeing this error:
Msg 297, Level 16, State 1, Line 1
The user does not have permission to perform this action.
By default, users cannot select from sys.dm_exec_connections. You would need to grant your users VIEW SERVER STATE in order to use the DMV, which I would not recommend. You have the option of signing your trigger with a certificate. It is not a trivial process the first time you do it, but after you do it once it's a piece of cake to understand and maintain. Here is the tutorial I would recommend following:
http://msdn.microsoft.com/en-us/library/bb283630(v=sql.90).aspx
Do not worry that it says "Stored Procedure", I am pretty sure you can sign triggers as well in the exact name manner. I have used certs to elevate a database user's permission level but never to grant server-level perms. The documentation says it is possible. From the article:
You can create a certificate in the master database to allow server-level permissions
There are no special teachers of virtue, because virtue is taught by the whole community.
--Plato