Normally, it would be a symptom of a non-functional network connection, when the Apple TV (2nd or 3rd generation) only shows Settings and Computers. All the other ‘apps’ are loaded from remote servers, after a cold restart.
… even while on a stable and working Internet connection.
How did you determine that? If you mean other devices on your home network, then it could be a settings issue for this device. Does it say to have an IP address in the range that your router is supposed to lease?
It hasn’t been used in a while
Could it be that this unit has a failed activation? See: Settings﹥General﹥About﹥. If the activation considered Failed, then the last line on that screen would say so.
Try resetting the unit to factory settings, then set it up again “as new”.
If activation won’t happen, then consider this workaround: discussions.apple.com/thread/253315520.
Regular signing in (for iTunes Store) may require a workaround for Apple Accounts that have two-factor authentication. See: discussions.apple.com/thread/251787405.
This exercise may be fun for a few, but frustrating for many.
It is a model from 2010, with very little functional use in 2025. Many third party apps have been removed as the content providers have changed their working protocols, and the apps have become incompatible, and have then been removed for that reason. The unit has had its last software update in 2014 (v6.2.1).
Such electronics have a limited lifespan. Apple and third party content providers may change the compatibility of the remote servers at any time for old unsupported hardware, making communication impossible when that happens.
Watching iTunes Store movie purchases may still be possible, I think.
iCloud services have been cut off for legacy models since late 2023. discussions.apple.com/thread/255664587
It is like trying to use an iPhone 4 in 2025 — the App Store has nothing for you, the browser doesn’t render modern sites correctly, the telecom providers have nothing for you. It is just technically obsolete.