my apple tv won't activate with sony kdl-40hx701

Does it start up ok or do you mean you get no video at all?

If just black screen then

Check these troubleshooting steps:

http://support.apple.com/kb/HT1551?viewlocale=en_US&locale=en_US

Specifically I wonder if the AppleTV may be trying to connect with an unsupported resolution giving a black screen. Try cycling display resolutions using these remote commands in step 6:

If your TV screen appears fuzzy or black (you see no video)

1. Make sure the television you are using supports the Apple TV resolution requirements. Please see the Apple TV technical specifications.
2. When you connect power, check to make sure the LED turns on. If the LED is not on, then verify with a known good power outlet or connect something else to the outlet you're using for Apple TV and make sure it works (such as a lamp or clock).
3. Make sure you're using the correct video cables and that they are connected firmly to Apple TV and to your TV.
4. Connect the HDMI cable directly into the Apple TV and your television, remove any third party devices or adapters.
5. Make sure the input setting you've selected on your TV matches the input you have your video cables connected to. See the documentation that came with your TV for more information.
6. Change the Apple TV resolution by pressing and holding the Menu and Up button for six seconds. The Apple TV will automatically cycle to the next resolution at approximately 20 second intervals. Pressing the Select button will immediately cycle to the next resolution.
7. If you are connected via HDMI, try unplugging and replugging your HDMI cable.
8. If HDMI isn't working on an Apple TV (1st generation), try component cables instead (and disconnect the HDMI cable temporarily). Read more about HDMI vs component video.