We are still assuming that ET is around our age, perhaps a little older or younger.
But what if ET is a billion years older? No matter where in the galaxy he may hail from, his technology would seem like magic to us, surely able to pick up our feeble attempts at sending out any signal. He could be watching re-runs of Hogan's Hero's right at this very second. This kind of ET would want to colonize the galaxy if it hasn't already done so.
The laws of physics exist. There are limits to what technology can do. If a civilization's technology reaches those limits, another billion years won't get it anywhere beyond them.
There is no reason to believe that there is a way for them to detect our signals at this point. Its like saying, "if ET is a billion years old, it should have mastered the Force and felt our presence by now."
There's no more reason to believe that the particular magic technology you're assuming is possible than that "the force" exists.