Longer exposure is the key.
Funny how sensitive the camera is, I generally have to turn the brightness down to the point that it would be unwatchable with the naked eye.
I got a Flip Mino HD camera last Christmas and it works really well for videoing TV, much easier than the older Sony DV 8mm since there are NO adjustments you can make except Zoom.
The downside is it makes huge files that need a ton of processing power to watch on your PC, the MP4 format is hard to edit and convert too.
The good thing is it can be uploaded directly to YouTube without hassle and in HD quality up to 720p.
Here's a Flip Video:
http://www.youtube.com/watch?v=EykM_lam17c
You can see a faint bar roll upward at intervals but it's not bad.