MD88 FLT CREW HAS ACFT ROLL FORWARD DURING ENG START AT SAT.

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INCIDENT OCCURRED ON JUN/THU/03 INVOLVING AN ACR X MD88 AT SAN ANTONIO ARPT IN TX. OUR CALL SIGN WAS FLT XXXX. THE FLT WAS SCHEDULED FROM JACKSONVILLE; FL; TO DALLAS; BUT WAS SUBSEQUENTLY DIVERTED TO SAN ANTONIO DUE TO TSTM IN DFW. ARRIVING IN SAT; WE WERE PARKED AND SVCED ON THE RAMP; AWAY FROM THE GATE. WITH SUBSEQUENT CLRNC TO DFW; WE STARTED BOTH ENGS IN THE CHOCKS. AS THE SECOND ENG REACHED GND IDLE; I (FO) NOTICED THE ACFT STARTING TO ROLL. I IMMEDIATELY HIT THE BRAKES AS A PWR CART WAS POSITIONED OFF THE NOSE TO THE R. THE STOP WAS ABRUPT; BUT NO CONTACT WAS MADE WITH ANY GND EQUIP FOLLOWING AN INSPECTION BY GND PERSONNEL. THE CAPT'S ATTN WAS DIVERTED BY GND PERSONNEL AS THE SECOND ENG CAME TO IDLE. THE CHOCKS WERE IN DURING THE EXTERIOR CHK; BUT WERE REMOVED SOMETIME PRIOR TO ENG START. ADDITIONALLY THE PARKING BRAKES WERE NOT SET. IN RETROSPECT; THE BRAKES SHOULD HAVE BEEN SET; SINCE WE WERE NOT HOOKED UP TO A TUG DURING START. ACFT ROLLED APPROX 5 FT. DEV FROM THE NORMAL ROUTINE DURING ENG START COMBINED WITH FATIGUE FROM WX DIVERSION CONTRIBUTE TO THIS INCIDENT.