Windows – Apple TV 3G can’t connect to Windows iTunes home sharing library

I'm trying to connect my 3rd generation Apple TV to iTunes on Windows 7 via iTunes home sharing, but when I "click" the Computers icon on the Apple TV, it shows an error message stating that it can't connect to my iTunes library. Connecting to the iTunes library on my Mac works. The only thing that doesn't work is using home sharing to get data from my PC iTunes to the Apple TV directly:

Here's what works:

• Streaming data from my Mac to the Apple TV via home sharing
• Streaming data from my PC to any device except the Apple TV (Mac iTunes, iPad Music and Videos apps)
• Streaming data from any device to the Apple TV via AirPlay
• Remote controlling my PC iTunes via the iPad remote app. I can even tell it to stream the data from my PC to the Apple TV via AirPlay.
• When remote controlling the Apple TV via the remote app, it shows my PC's

What I've tried:

• rebooting the Apple TV
• rebooting the Windows PC, reinstalling iTunes there and checking
• disabling the firewall on the PC (even with the firewall enabled, all other devices connect to the PC flawlessly)

Any suggestions?