I am a relatively new Mac user and have also just purchased Apple TV. I have used HandBrake to convert some movie files to Apple TV format but when I watch them I get crystal clear sound but no picture - only a white screen. Has anyone else encountered this and found a solution.
Does your

TV show a picture otherwise? For example, can you see the user interface? Can you play a movie trailer in the movie menu? This should confirm that you don't have a video cabling problem.
Assuming you otherwise see a picture from your

TV, did you use the Handbrake

TV preset when you converted your DVDs?
If yes, try opening the file on your Mac and see if it has picture & sound there. If so, you'll know the file itself is probably OK. Import it into iTunes, then try to play it back in iTunes. Is it playing there?
If it will play in iTunes, I suggest a simple experiment. Use iTunes, Advanced menu to "Create Apple TV version". This will take a while as it is re-doing what you did in Handbrake again. Will the resulting file play on

TV? If so, you are having a problem with how you are using Handbrake. Be sure to select the

TV preset when you try again. Note if the "Create Apple TV version" test works, you don't want to decide to just do that from now on for 2 reasons: 1. it will take about double the time to render all your movies, and 2. rendering in Handbrake then again in iTunes is trading picture quality to compress and then compress again. This is just a test to help zero in on the cause of your problem.
Handbrake works very well for yielding a movie (in one round of conversion) that will play as desired on the

TV.