Apple TV 1st Gen can no longer connect to wireless networks

My Apple TV (1st Gen) has recently lost the ability to connect to either of our wireless networks at home. I rean the diagnostics at the reset screen and the Apple TV says it is performing normally. In the settings, whenever I attempt to connect to a wireless network, I am now only offered "Other..." as a choice. Proceeding to the next screen, I enter the name of the network closest to the Apple TV -- an Airport Extreme set up for 5 GHz that this Apple TV connected with daily up until 2 days ago. The Airport base station is perfoming normally, as my MacBook Pro can see it and establish a network connection without any difficulty. The issue is limited to the Apple TV. I did a Factory Restore, and now when I go to Wireless Network > "Other..." > Enter the name of the wireless network" the resuit is always the same, and error message stating: "There was a problem connecting to the network. Check your settings and try again. (-4)".

This message comes up almost immediately, without requesting a WiFi password -- suggesting to me that this Apple TV has lost the ability to connect to ANY wireless network due to a hardware failure.

Q: Has anyone else in the Support Community had a similar experience with their 1st Gen Apple TV, and if so, did you find a solution to it?

Note: When I first noticed the connction to this Apple TV had gone stale (greyed out in the iTunes Airplay Speakers list), and prior to doing the Factory Restore, I could play back iTunes content stored on the hard drive, but could not connect to the local wireless networks. I noticed that the Apple TV was running very hot -- it has alwasy run pretty hot to the touch.

If this Apple TV has died, I will get a 3rd Gen Apple TV, but wiill then have to work through the HDMI to Composite video + Audio issues, as this Apple TV is connected to our older (non-HDMI) TV.