Honestly, chances are, it's not worth pursuing via Law Enforcement. If they never really got in, then no one is going to be interested in pressing charges.
But you can pursue it through the originating ISP. Gather as much information as you can and email the logs to whatever the ISP's Abuse@ email address. Be sure to include all appropriate TimeStamps as well as what TimeZone you're in.
Don't threaten them (unless you actually have the power to pull the threat off*) but tell them that a user on their network has violated the ToS/AUP of their service and you expect them to take whatever measures necessary to prevent it from happening again.
Chances are, you'll never hear anything back, but you'll probably never see an attack from that IP again.
*If you work for a public utility, you can threaten ISP's. As interference with a Public Utility is frowned upon by the Fed's and ISP's hate having the Fed's show up and want to see their logs. It's amazing the number of IP's that have never shown back up in my logs.