Somehow the relay isn’t switching. Make sure all the components in the relay circuit are installed properly. Use a magnifying glass to check for shorts around those transistors and diodes. It sounds like it wants to switch, but one of the coils is being held high and not allowed to go low. Other than these suggestions, I don’t know what is causing it. You may have to pull the transistors off the board and manually toggle the relay (with jumper wires from the 5v rail) to ensure it works properly.
Good luck!
-Brach