  Effects of non-magnetic disorder on the critical temperature T_c and on
diamagnetism of quasi-one-dimensional superconductors are reported. The energy
of Josephson-coupling between wires is considered to be random, which is
typical for dirty organic superconductors. We show that this randomness
destroys phase coherence between wires and that T_c vanishes discontinuously at
a critical disorder-strength. The parallel and transverse components of the
penetration-depth are evaluated. They diverge at different critical
temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and
phase-coherence breaking respectively. The interplay between disorder and
quantum phase fluctuations is shown to result in quantum critical behavior at
T=0, which manifests itself as a superconducting-normal metal phase transition
of first-order at a critical disorder strength.
