Cyclone 2 FPGA Starter Board Issue

The fact everything work in the RUN mode shows you don't have any hw failure.

The dimmed LEDs almost surely mean they are driven with a modulated signal (i.e. a square wave) rather than a steady logic level.

This could indicate that you are loading a wrong sof file, belonging to a project where those LED pins are used for anything else.

Do you use a precompiled sof file or did you regenerate it from Quartus project sources? In the second case, probably you simply need to check pin assignments.