  Effects of non-magnetic randomness on the critical temperature T_c and
diamagnetism are studied in a class of quasi-one dimensional superconductors.
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 the wires and T_c vanishes
discontinuously when the randomness reaches a critical value. The parallel and
transverse components of the penetration depth are found to diverge at
different critical temperatures T_c^{(1)} and T_c, which correspond to
pair-breaking and phase-coherence breaking. The interplay between disorder and
quantum phase fluctuations results in quantum critical behavior at T=0,
manifesting itself as a superconducting-normal metal phase transition of
first-order at a critical disorder strength.
