The number of potential abodes for "life as we know it" getting ever bigger helps in the odds game of the Drake Equation somewhat, but there's still some HUGE downward pressures on the chances of making some sort of SETI contact.
Earth spent a looooong time, the lion's share of it's geological history, close to 90% from the end of the Hadean to the Paleozoic where the first vertebrates start showing up in the fossil record. There's no reason to believe other planets might be even slower, but there's no reason to believe they'd be faster in turning up complex life either. Planets that are more stable than Earth environmentally might turn out life faster, OTOH, without upheavals, ice-ages, asteroid/comet impacts, supervolcanisim etc. there might not be any selection pressures for things to "get interesting" either. OTOHOH... Planets that are too violent might have the same result, mass extinctions that keep resetting the clock back to single-cell organisms.
There's also nothing in evolution that points towards intelligence or tool using as being "goals". Evolution is a blind process and does not have any "goals" at all, other than adequacy and the filling of environmental niches.
That said, billions of planets seems like good odds for at least one other intelligent tool using, technological species to arise somewhere, sometime in the galaxy. However, assuming radio transmissions at light speed, it's still infinitesimally slow as compared to the scale of the Galaxy.
http://jackadam.net/misc/radio_broadcasts/radio_broadcasts.jpgThe sphere defined by the light-front of ANY purposeful brodcasts from Earth is only roughly 200 light years in diameter. If we were to try and "detect ourselves" at this distance, an all out effort on our part to build very large spaceborne VLBI arrays might just barely be able to catch a faint snippet of artificial carrier radio signals. POWERFUL broadcasts like 1950's over-the-horizon Cold War radars that only need radio dish arrays the size of whole planets rather than the size of whole solar systems, are only half of that distance. And our history of RF leakage into the galaxy is also constantly getting weaker by the light-second due to the inverse square law. And as our technology advances, fiber optics, directional tight-beam radio, digital spread spectrum technology etc. means our signals are getting weaker, not stronger. We are already "going dark" again to some degree.
One thing that's not talked about is that even the most sensitive instruments given over to SETI work, unless the transmitting species is within just a few hundred light years of us, the physics of the thing suppose an alien race that wants to be heard very badly and builds a radio transmitter that harnesses the energy output of entire stars.
Granted, we've barely begun to LOOK, but so far there also seems to be a lack of Dyson Spheres, Von Neuman probes, or evidence for any Kardashev Type II or III civilizations, which are things we could see at considerable distances across our galaxy, or find right here in our solar system. There are definitely none yet that are actively trying to attract our attention. (conspiracy theories notwithstanding) And that kind of belies the Fermi Paradox arguments that it would only take one long-lived surviving technological species to cover our galaxy, even at just a fraction of light speed, and we should know of them.
My gut feeling is that there is at least a handful of intelligent tool-using species in our galaxy at any given time, but not all of them "make it", and those that do, the technology level needed to meaningfully challenge interstellar space is so high, it fundamentally changes their paradigm of existence to the point we can't see them, or have any basis for understanding what it is they do. So rather than "Star Trek", think "The Monolith Makers of 2001", except those species don't even leave the monoliths laying around for us to wonder what they are.
