Debug Bricked Standing Desk IC Board Issue
The clicking sound is made by the electromechanical relays on the board (4 black boxes). They have electromagnet inside and it attracts the two or more contacts (they connect/disconnect in order to control the current flow). This switching of contacts is what You hear.
The board might have faulty power semiconductors (if there are any) controlling the motor. Microcontroller probably tries to start the cycle couple times until it sees that it is impossible to move the table.
The fault might be in a board or in the motor (the brush had lifted for example). You would have to had some electronics knoweledge to repair it. It's probably easly flexible.