Thank you for the suggestion. I will try it out.
On the intel (iMac7,1) Mac OS Snow Leopard, with iTunes 11.4, I have installed Aqua Proxy, from mavericksforever.com It has a readme with instructions inside. This helped solving the "no internet connection" error. iTunes now can see internet connection and connect to iTunes store. It shows the content, plays previous, etc.
Now the issue is that if I try to log in, or enable genius on new iTunes library, it blocks it, saying "update to newest iTunes version". Of course this is not possible on the old system. I tried to spoof the iTunes version, by editing the plist files, with new version numbers, but that did not work. iTunes servers still recognized iTunes 11.4 as an old application.
Temporary workaround that worked: I used an old iTunes library folder, that I have backed upped previously, and it had genius originally enabled. I removed all the media files, and added everything fresh. Then I connected to iTunes store, and clicked on menu item Store > Update Genius. This then prompted iTunes to update Genius information, and the genius mixes and playlists worked after the update. But it worked only because the library already had genius enabled.
Now I need to figure it out how to work around this "update to newest iTunes version" and spoof the version numbers. I think it is the only reason it does not allow to log in with old iTunes. With this solved, I could log in, and then genius can be enabled on new libraries, and also iPod apps should work as well.
Things I will try. Obviously, without logging in to iTunes store, I will not be able to sync my legal ios games, that were purchased. But I will try to sync some cracked ipa files to some jailbroken ipods and see if that works.
ps sorry just realized this is ppc thread, not intel..