AN EMB135 PILOT REPORTS STARTING THE TKOF ROLL WITH AN ENG NOT STARTED BECAUSE ATC DISTRACTED THEM WITH TAXI INSTRUCTIONS AND COM INFO REQUESTS.

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TAXI OUT WITH NEW CONSTRUCTION SINCE MY LAST FLT. GND CTL ADVISED 'TAXI-SLOW' FOR UNKNOWN REASON. WE DID. APCHING ACTIVE DEP RWY; ADVISED TO SWITCH TO TWR. ENTERING RWY WE WERE ASKED TO 'TAXI-FAST.' APPEARED WE WOULD BE RELEASED SHORTLY. OUR CUE TO STARTING #2. (SE TAXI; NORMAL TO MINIMIZE EXCESSIVE FUEL BURN -- A DELAY PRONE ARPT FOR US.) FOLLOWING REQUEST TO 'TAXI-FAST' LCL CTLR ASKED US TO COME UP ON 122.75. HE HAD INFO FOR US. THE NIGHT BEFORE WE HAD BEEN DELAYED 1 HR DUE TO A RWY CONFIGN AT OUR DEST THAT SHUTS DOWN DEPS FROM AN ON-GOING FRUSTRATING EXPERIENCE FOR US. THIS CTLR IS SYMPATHETIC AND HAS TRIED TO HELP OUR CAUSE. HE WAS ON DUTY THE NIGHT PRIOR DURING OUR DELAY. HE WANTED OUR PHONE NUMBER FOR CONTACTING US LATER WITH FURTHER INFO. SO; WE ARE SE TAXIING ON ACTIVE (BACK TAXIING DUE TO CONSTRUCTION). PLT MONITORING (CAPT IN R SEAT) IS OFF FREQ AND I BECAME CONCERNED WE WERE OFF TWR FREQ DUE TO HIS SWITCHING HIS COM TO OTHER RADIO CONFIGN. I COULD NOT SEE ACTIVE FREQ. WE RESOLVED THAT ISSUE. HE CAME BACK ON TWR FREQ; TWR CLRED US FOR TKOF REACHING RWY END. A CONFUSING; RUSHED SITUATION WITH MANY DISTRS. WE COMPLETED CHKLIST; I TURNED AROUND AND BEGAN ADVANCING PWR. IMMEDIATELY I WAS AWARE SOMETHING NOT RIGHT. ACFT SLUGGISH; PULLING TO R. PLT MONITORING (CAPT; R SEAT) NOTED #2 ENG NOT RUNNING. WE SLOWED -- A LITTLE PROGRESS (100-200 FT) ADVISED TWR WE NEEDED TO RESET EQUIP TURNED AROUND; STARTED #2 ENG AND REACHING RWY GND ONCE AGAIN; WE COMPLETED CHKLIST AGAIN AND TOOK OFF UNEVENTFULLY. AN EMBARRASSING SCENE. I HAVE HEARD RUMORS OF OTHERS IN SAME SITUATION; BUT HAVE NEVER EXPERIENCED THIS BEFORE MYSELF. OUR ACFT HAS NO ANNUNCIATOR/EICAS LIGHTS IF ENG IS SHUT DOWN NORMALLY OR IS NOT STARTED IN THIS SE TAXI CONFIGN. WE MODIFIED OUR CHKLIST THE NEXT DAY TO ADD A CONFIRMATION OF 2ND ENG STARTED TO LINE UP CHKLIST.