Nearly all lab supplies will have a reverse-biased rectifier diode across the output terminals. In some "normal" usage cases, this will prevent a reverse voltage from appearing across the terminals, which could damage various components (output transistors, output capacitors, etc.). Such a case is when using two supplies in series (to get higher output voltage), and one goes into current limiting mode, while the other continues to try to push more current.
Anyway, this diode is easily damaged by doing things like connecting a powerful battery or another power supply in reverse, or sometimes even just by using the supply/supplies in "normal" series operation. I've seen 1 A reverse diodes on a 3 A supply! You can imagine what would happen in the above scenario if the second supply is pushing 3 A through a 1 A diode.
Rectifier diodes usually fail short circuit. Of course, not a perfect short, but with some resistance (it is a semiconductor after all). Based on the symptoms you see, I would strongly suggest looking for this diode and testing it. You can check if the diode is the problem simply by removing it (or lifting one leg), then testing the supply.
You could also test it with a multimeter in diode test mode. Turn off and unplug the supply. Short the terminals (to discharge the output capacitor, just in case) then remove the short. With a multimeter in diode mode, connect test leads to the + and - outputs of the supply. Test in both directions. If the diode is good, the meter will show approx 0.6 V forward voltage (a good diode) in one direction, and open/over limit in the other direction (it may start low and slowly climb up, as the output capacitor of the supply is charged by the multimeter test current). If the diode is bad, you will measure 0.6 V or lower in both directions.