There's probably a million ways to acheive the effect you want. For the beam of light you'll need something like Trapcode Lux, won't give you particles of dust but will give you volumetric light. There's a bunch of other ways to acheive the effect but I feel Lux is the easiest.
To put out light to show on the sides I would set up a light on facing from the screen, for an easy (but not as accurate) effect just set a wiggle expression on the intensity. For more accurate you could set try putting the light behind the video screen and using the screen as a gobo so the light actually comes out accurately.
Hope that helps.
Jeff McBride
Motion Graphic Designer/Editor
LimeGreen
Chicago, ILwww.limegreenproductions.com