I bought a SATA to PATA adapter to solve the interface problem. I cloned the drive and the Apple TV booted perfectly from the new one. My only problem is enlarging the media partition, which is the whole point of me upgrading the hard drive. I used Disk Utility, but I couldn't enlarge that partition. But now I don't need to use the old Apple TV because I finally got a new projector which has HDMI, so now I can use my newer Apple TV.
By the way, I had my first generation Apple TV connected to my projector with composite cables and I used HDMI to DVI and DVI to VGA adapters to trick the Apple TV into using color over composite cables.