It's quite common for circuits to work with capacitors that are significantly degraded. Capacitors are often specified with larger values than needed to allow the system to work when the capacitors have lost some of their capacitance.
Electrolytic capacitors will degrade with time, especially if they are hot, whether they are used or not. Degredation can be loss of capacitance, but it can also be increase in internal resistance.
The output filter capacitors may generate more heat, and fail quickly, if they are not large enough or have too much internal resistance. The degradation during storage could have taken them to the point where they failed very quickly as soon as the power supply was used.