Thank you very much.
If we're talking about reruns of old programs, or just a videotape,
and likewise if it's in a place where no one can see you, or alternatively if it became widely accepted that television is like an air conditioner,
would there still be a problem?

Even reruns are operated by a whole system of people. With a videotape, clearly there is no problem (essentially; the issue of appearance to onlookers exists here too).
And even if no one can see you, something forbidden because of appearance to onlookers is forbidden even in private rooms.

If the prohibition is rabbinic, I seem to recall that Tosafot in Moed Katan wrote that this rule does not apply even in private rooms.

Tosafot, Ketubot 60a, s.v. “Mema'akhen.” But that does not seem to be the view of most halakhic decisors.
See, for example, this nice overview here:
https://www.etzion.org.il/he/%D7%99%D7%91-%D7%9E%D7%A8%D7%90%D7%99%D7%AA-%D7%A2%D7%99%D7%9F

And for the air conditioner to work, aren't Jews also working at the electric company?

Definitely yes, but there it is necessary because of saving lives. Beyond that, it is adding more than the minimum required, and that is not free of problems. Of course, electricity on the Sabbath is a much more vital need nowadays.

Does the fact that this is a vital need nullify Jewish law?

It does not nullify it, but it does make it possible to rely on lenient opinions and on doubts.