With tightvnc that will not be possible.
But if you use my tigervnc package instead (http://slackware.com/~alien/slackbuilds/tigervnc/
) you can use the included x0vncserver to export your already running X session.
Remove tightvnc, install tigervnc. Then, set a password and start the x0vncserver like this:
From another computer you can now start a vncviewer and connect to "yourcomputer":
The password that you just configured is the password that has to be entered in the vncviewer.