You on XP or Vista?
If the other machine is using the same operating system you can carry out the same steps on each of them and set the other monitor as the primary one. I've had to do it before!
So you'd do something like right-click on the desktop (you have to guess and hope you're right-clicking on the desktop), and then click the down cursor 6-times - then click enter - then click the right cursor 4 times - click tab twice - then click down cursor once - then click tab 7 times and hit enter.
Voila.
Of course, this is necessarily guaranteed to work.
(Now someone will come along and give you a much easier way of sorting your problem

)