It appears you are missing the point I am trying to make. The current technology will not get us very far, I am unfortunately very aware of this. Also the best chance, under our current understanding of the universe is the Alcubierre drive and that would use up something along the lines converting Jupiter's mass to energy.
To get back to my analogy, we two are living in the bronze age. I say traveling the sea will be the future and you say that on our current technology (canoes) we will never be able to cross the ocean.
There is no reason why we can not get a closed loop system to sustain itself. Also there are potential improvements in current rocket technology or rather propellant. Sure we will probably not leave our solar system withing this millennia, but there is no reason why we can not go out into our solar system.
Finally, if you take Project Orion, technology from the 1950s, you get a trip time of 133 years to Alpha Centauri. Although it exceeds a lifetime of a human, it is not completely outside of your reach. It has a few other issues, such the radiation and life support for such a trip, but it is not fully outside of the reach of what we can do.