If you are limiting communicating civilizations to a 1000 years, then you effectively saying civilizations either destroy themselves or some sort of technological singularity occurs in which they effectively leave the known universe. 1000 years is nothing in the scale of galactic time scales.

We can already envisage creating self replicating (von Neuman) probes that could travel between starts at some modest rate (say .05 speed of light). If one civilization in the whole galaxy launched such a probe, it could visit the entire galaxy in a relatively modest time frame (galactically speaking--say on the order of 100,000 years). Given that with the number of older stars around, you would think some civilization would have reached the relevant technology levels to do such things a billion years(and every other time frame up to now) ago. Why haven't we seen any such artifacts? Hence, the fermi paradox remains.