When I'm recording video, if a light shines into the camera, a vertical line shows up on the recording. How do I stop that from happening?

I know it's not because of something smeared on the lens of the camera. It's an actual recording issue. I don't want to have to change how or what I shoot to keep the line from appearing.

Well, you really don't want light shining into the camera. That's called a backlight situation and it'll cause your subjects to be in shadow. Now, you may want do that deliberately, sure. But you're not talking about the best video camera here. In many ways, video in a digital still camera is more marketing feature. The video quality is just a hair better than VHS, the audio tinny. I think in the conditions you want to shoot at, your expecting far too much out of a CCD chip which is mostly designed for still pictures. You may be able compensate by shooting with the light on your subject, rather than into your lens or by bouncing the light onto your subject.