During taxi to the runway, the Captain reported that he originally planned to back taxi on the runway, but he observed a gyroplane waiting to takeoff and decided to taxi on the closed taxiways to allow the other aircraft to depart. As the taxi progressed on the closed taxiway, the Captain reported that his First Officer stated, "Watch that left side!" When the Captain looked to his left, he observed the left wing of the airplane strike a construction vehicle that was parked next to the taxiway. After the collision, the Captain stopped the airplane and shutdown the engines on the taxiway. The Captain stated there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation. The left wing sustained substantial damage. The Captain stated that there were no barricades present on the closed taxiways, and the construction vehicle was not marked or flagged. The Captain also reported that he checked the notices to airmen (NOTAMs) during preflight and was aware of the taxiway closures at the departure airport. During postaccident interviews, an employee of the fixed based operator (FBO) stated that he moved the barricades on the closed taxiways earlier in the morning so that another airplane could depart. The airport manager stated that the taxiways were published closed and he did not provide any instructions to move the barricades.