EMB-505 / Phenom 300
Flight Crew Air Transport Pilot (ATP)
Situational Awareness
Aircraft Equipment Problem Less Severe; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown
Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Human Factors
I went out to pre-flight the aircraft while the Captain remained in the FBO to print out the flight plan; etc.  In performing my cockpit preflight checks; I missed the fact that the Hydraulic Pump switch was in the OFF position; rather than AUTO (which is where it had been when we left the aircraft the night before); because Maintenance had been working on the aircraft's brakes overnight.With the passengers on board; I went through the Before Start checklist while they were being briefed by the Captain; and initiated the Engine Start on Number 2 as he came up to the cockpit and strapped himself in. As Engine 2 came on line; I saw ramp staff waving to indicate that the aircraft was moving. Both the Captain and I hit the toe brakes; and then he tried the Emergency Brake; but without hydraulic pressure; the aircraft continued to move. The Captain took the controls; instructed me to contact Ground Control; and steered the jet toward the taxiway; away from parked aircraft. He attempted to start Number 1 engine as we moved; hoping to fix the problem that way; but due to the aircraft's configuration; the start was unsuccessful and he had to shut it down. As we taxied onto A taxiway; the possible source of the problem finally occurred to me and I asked the Captain to check the Hydraulic Pump switch position. Braking was quickly restored and I informed Ground Control; but they responded that they'd received a call from [the FBO] advising that we'd left with the GPU (Ground Power Unit) still attached; and that the GPU access door was still open. I got clearance to taxi back to the ramp.Once the aircraft was parked and Number 2 shut down; we discovered that the mounting plate for the plane's electric receptacle had been damaged as we moved with the GPU attached; before the electric cable had pulled loose. The GPU was not damaged.
EMB-500 First Officer reported they were unable to stop the aircraft after it began moving on the ground during engine start due to the hydraulic pump switch in the off position.