finding computers that users logged onto

Is there a way to find out all of the computers a particular user has logged onto? This is in a Windows NT domain environment. One way I know of will only find one of the computers a user has logged onto that is to go to a command prompt and
net send username any message after sending user a message at the command prompt type nbtstat -c and on the line of the username you sent a message it will show you the IP address to the computer the message was received at. The downside to this method is it will only find one of the machines the user has logged onto. I know of a program called goverlan that among other things will list all of the computers a user has logged onto but I can't afford that program and want to know if there is a better way. Thanks