HT1595 apple TV cannot connect to internet

Question

apple TV won't connect to internet

Answer 1

I've had this problem for ages, which seems to have started with problematic download speeds and then resulted eventually with the inability of the ATV (2) to connect to the internet.  Like you, we were able to connect to the wi-fi network in our home, and able to connect to the computer, but our ATV was not able to connect directly to internet services or internet products available through its connection with iTunes (eg: movie rentals on the computer).  Every other wi-fi device in the house was connecting successfully, the ATV did not. 
Prior to that time we'd been operating the device successfully for about 15 months.
Most web advice seems to suggest problems with  static IP addresses, or blocked 80 and 443 ports.  We've talked with Apple support, ISP support and Netgear support.
In the end, by adding   together clues given by Apple and Netgear, we worked out that the recently updated software for ATV is no longer compatible with the software of our modem router.
By updating the modem router's firmware (which was a process in itself!) our ATV is back to full functionality. 
You can update your modem or modem/router by going to the home page of its manufacturer (eg: Netgear).  Model numbers and Serial Numbers are normally recorded on the bottom of the device, as is the address used to access the modem router manager, in which you can update your device.
Hope this is useful to others.