I purchased a Belkin HDMI to DVI cable at the same time I bought the ATV2 (from the Apple Store). This cable only sends video to the TV, from the ATV2. I then used the Optical Audio (Toslink) out of the ATV2 to a Gefen converter (Optical Audio to RCA red and white audio cables) and plugged those into the RCA audio input on the TV.
This worked fine for me (i.e. no streaming or HDCP errors), prior to any updates of the software. After doing the updates, my ATV2 would only produce a 480P resolution. Now if you have seen the difference between 480P and 720P, you would not be happy.
I then purchased the HDMI Switch and a 24AWG cable from Monoprice.com. I plugged the new HDMI to HDMI cable into the ATV2 and the switch. I then connected the previously used HDMI to DVI cable into the TV to provide video. The switch also has RCA (red and white) audio out. I plugged those into the TV for the audio from the switch. I ran the video and audio directly to and out of the switch. Nothing through an audio system.
Turned on the switch, the ATV2 and then the TV. Checked the resolution setting for the ATV2 and I had 720P. Very happy. I then streamed a full movie from my iTunes library and it worked fine. I then streamed a HD movie from Netflix for 90-minutes. No problems.
This switch and set-up worked for me. It may not work for you. Switches can be problematic at times. I took a shot and it worked.
I hope this helps you to get your ATV2 up and running.