It's unbelievable that soon we will have a SETI program running that can detect, within 200 light-years, any signal that was originally as weak as an aircraft radar ping is on Earth; it means that if there were such radars operating within 200 LY cube around these 10k normal stars (not counting brown dwarfs), they would be detected.
Of course you have to keep in mind that most SETI researches now believe that a sentient civilization may only exist in our current post-industrial primitive form (before hitting singularity or death) for a short time, so a negative signal would actually tell us a lot on the upper bound for how many such transitional civilizations are out there.
But there are couple of additional reasons why this may just work; the most important than any - singularity never happens and technology rapidly plateaus then we would find a signal!
Recently scientists have started believing that the black-hole singularity is actually no singularity; it is just a breakdown of our current physics under such extreme conditions. Similarly, we now know now that there is a limit for how dense and big our biological brains can get before they stop getting smarter. The speed of light is a fundamental limit not just for space-crafts making star-trek difficult at best, but is also a major handicap for how smart an AI can be, due to literally a speed limit on how fast processors can run (true an optical processor will be 100 times faster than an electrical one due to speed of light being higher than electric current, but it is not that much more). The promise of quantum computers seems more like relegated to specialized computations. Moors law has also come to an end for chip-densities as we hit the scale of individual atoms.
There are signs everywhere that the universe does not like singularity. However, it does not mean that things will not get really advanced tech-wise, it just means that there will be no singularity, and technology will advance much more at star-trek pace than at a pace that destroys our world and causes singularity as recently warned by several influential thinkers, including Ray Kurzweil, Elon Musk, and Stephen Hawking. Though there have also been thinkers such as Carl Sagan, and Michio Kaku that probably would agree to this more hopeful view I am proposing here.Why would a tech plateau be good for longevity of Earth-like civilizations? It may give the needed time for our brains and social fabric to mature with technology thus preventing us from destroying ourselves. Contrary to what scientists estimate right now (see article above), we may keep using radars for 1000s of years (albeit in more advanced manner), and their intensity might increase as every ship, air-craft, car, and space-craft starts using self-driving robotic tech. Additionally our populations would grow because of longevity and cure of aging (no singularity needed there as the tech is relatively simple), yet our not-so-advanced tech requires huge resources making us easily expand within our solar system. This would again dramatically boost the number of such weak signals emanating from millions or billions of devices.