That doesn't work. If a civilization reached slightly beyond our tech level around twenty million years ago (a blink in the eye as far as the universe is concerned) anywhere in our galaxy then we should expect to have seen some sign of them. Radio and visitation aren't the only issues. We don't see any evidence of Dyson spheres or ringworlds (although the second is something we've only recently been able to detect- Kepler should be able to detect ringworlds albeit I don't know if anyone is looking for them.) We see no evidence of any form of stellar engineering or large scale structures at all. And distance only matters when you look into the near past. Civilizations that have had millions of years to prosper should have spread much farther. Note that our galaxy is only about 10,000 light years across. (ETA: 100,000 not 10,000 see roystgnr remark below.)
100,000 light years across; you may be thinking of 10,000 light years thick.
But in any case, small enough for an expansive civilization to colonize, slower than light using nothing more "speculative" than fission-based rockets, in a fraction of a percent of the age of the galaxy.
One serious issue for evaluating existential risk is working out whether most of the Great Filter is behind us or in front of us. This relates to the Drake Equation and similar attempts to estimate the frequency of life in an obvious way.
Over the last few years, it has become increasingly apparent that extrasolar planets are common. However, what fraction of these planets lie in their stars habitable zone has still been an open question, primarily because most of our current methods for planet finding easily find planets that are either very large or are very close to their star (ideally both).
A new study, using the data from the Kepler spacecraft, estimates that about a third of all stars similar to the sun have at least one planet in the habitable zone. There are some issues with this estimate, and Phil Plait discusses them at his blog. The estimate has a large amount of variance. The paper actually estimates 34% +/- 14% and the issues that Phil brings up increases the uncertainty in both directions but it seems safe at this point to consider this not being very far off.
One obvious issue from a Fermi perspective is that some systems will likely have multiple planets in this zone. Also, having planets in the habitable zone is clearly not sufficient for life. By the standard estimates for habitable zones, Venus and Mars are both in the habitable zone of the sun. And there may very well be ways for life to arise outside the habitable zone. Moons like Europa and Titan seem to be excellent candidates, and we can't rule out more exotic forms of life in other habitats although that seems not too likely right now.
However, one thing this makes clear: The part of the Great Filter that is behind us that is due to planets not lying inside the habitable zone is small. So the question is, what does this mean for our estimates of how much of the Filter is behind us and how much is in front of us?