  We study numerically the interplay of phase coherence and vortex-glass state
in two-dimensional Josephson-junction arrays with average rational values of
flux quantum per plaquette $f$ and random dilution of junctions. For $f=1/2$,
we find evidence of a phase coherence threshold value $x_s$, below the
percolation concentration of diluted junctions $x_p$, where the superconducting
transition vanishes. For $x_s < x < x_p$ the array behaves as a
zero-temperature vortex glass with nonzero linear resistance at finite
temperatures. The zero-temperature critical currents are insensitive to
variations in $f$ in the vortex glass region while they are strongly $f$
dependent in the phase coherent region.
