Ex 5.5 Server Locks After Blocking Relay

I stopped relaying except for inside networks on our server a couple of weeks ago. Since then almost every morning we have to reboot the server. It is Exchange 5.5 on NT 4. The consultant who built it before I was hired created a system volume that is only 590 MB. The server is scheduled to be replaced next year, so spending money to upgrade it out of the question.

I checked the log and it shows a great deal of use by what look to be spammers around 3AM. I have a theory that their spamgets stored on our server in temp files, and since we no longer relay it for them, it quickly fills up all remaining disk space on the system volume. Am I correct? How do I resolve this other than daily reboots?