It's not clear to me what the symptoms are. Is it just the display reading zero, or is there actually no current flowing (check with DMM in series with the resistor)? Is the resistance low enough that the required amount of current can flow without exceeding the voltage you set? Does current limiting work in CV mode?
I'm surprised that you can select CC mode. Normally, you set both a current and a voltage limit. The power supply will limit both, and if one of them exceeds the limit, it will regulate that. If it limits current (eg. with terminals shorted), it will be in CC mode. If it limits voltage (terminals open), it's in CV mode. Not something you switch between yourself. Does CV mode mean that the current is limited to the max, and CC mode that the voltage is limited to the max? That doesn't seem very useful.
Looking at the schematic (top part control board, but the other one appears the same), it appears to me that the regulation is performed by IC12/13. D7 and D10 form an OR (assuming the anode of D10 is connected to the base of Q5), both can sink current from Q5, which decreases the base current through Q1-4.
I would probably check the input of IC12. If my guess is correct, I would expect to see the voltage around R15 change when you change the current limit, and the voltage of IS increase when any current is flowing (regardless of CV/CC mode). This problem could be caused both by the regulation around IC12 and the control, eg. IC10/11.
IC12 appears to responsible for current limiting, and is set to max. current when in CV mode. In CC mode, the current limit is limited by digipot IC10. IC13 appears to be for voltage limiting, although I'm not sure where CN7-3 comes from.
The CV light appears to be controlled by IC6D(?), which shows which of the two op-amps is actually sinking current, so it's not controlled by the buttons, but by the actual regulation.