Try to let the tv set search for the channel. Modern tv's offen are a little to sensitive, so the atari could also be at channel 2+ or 4-.
And don't forget to slide the switch to computer.
It'also could be the switch.
I tryed a computer-tv switch from my old nes and the only thing i got was a realy bad picture. When i tryed the switch of a colecovision, everything was allright.
You could also try to plug the atari staight to your tv without the switch.
The cablesignal could also influens the signal of the atari.
The only thing i don't understand is this line:
"Unfortantely, none of my TV's have the old style Antenna thing"
Does it mean that the tv's at your country haven't got an tuner with antenna plug? Cause over here in the Netherlands we still have the same antennaplug as was then in the 70's when the atari was on the market.