Many customers who access the internet have dynamic IP addresses, meaning that when they connect again, they are likely to have a different IP address. And certain ISP's like AOL, which use tons of proxy servers, cause a user to potentially have several different IP addresses while they are logged in.
In these situations banning an IP address by itself won't work, and banning an entire IP range would ban everyone coming from that ISP.
If you ban an entire range that covers an ISP, for example, you would probably want to lift it at some point. After a few months of being banned, the offender may find some other forum to bother. You then lift the ban, which allows everyone else from that ISP access your forum.
You could try the cookie thing and then show the same message as a banned IP Range. It would make him think you banned his IP address instead of placing a cookie, throwing him off. If he thinks his IP is banned, he won't bother deleting the cookies to try to restore access.
It's worth a try anyway.