Capacitor rated voltage vs supply voltage
Better replace your 1000/25 with 47uF as was in the original design. Be sure to use the same type - ESR, temperature, etc. Unless it is a very low power supply (less than 1-2W) I really doubt this capacitor is a "filter" one on the secondary output. It may have a different function and changing its value so radically you change how device handles its startup and protection. If you cannot find 47/16 you can put 47/25V or 35V, but be sure the capacitance is 47uF and temperature and ESR is like on the original.

The strange thing you are observing actually is not that strange. Probably the power supply tries to turn on for a second, goes to 23V, its feedback dont return the right signal and its shuts it self down. After a couple of seconds when its startup capacitor has been recharged it tries to start again.

If the supply's output was 12V it is very likely that you have a feedback fault issue. This feedback fault may have rasulted in output overvoltage and output capacitor failure. The fault may be a loose solder joint, some component in the feedback loop has failed - TL431, optocoupler, some resistor, and finally it may be the main IC.