B737-700 CAPT DID NOT XFER PWR FROM THE APU TO ENG GENERATORS. THEY HAD AN ELECTRICAL FAILURE WHEN THE APU WAS SHUT DOWN.

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AFTER ENG START; I PERFORMED THE FLOW WITHOUT XFERRING PWR TO ENG GENERATORS. I WAS DISTR BY THE REQUIREMENT FOR ENG ANTI-ICE WHICH I ACCOMPLISHED FIRST AND OUT OF SEQUENCE. THEN I MISINTERPED THE BLUE LIGHTS ON THE ELECTRICAL PANEL AND RESPONDED 'GENERATORS ON' DURING AFTER START CHKLIST. PRIOR TO TAXI; I TURNED OFF THE APU. THIS RESULTED IN A PWR INTERRUPTION BEFORE I SWITCHED TO THE ENG GENERATORS. DURING TAXI CHKLIST RECALL; THE FLT CTL LIGHT REMAINED ON. THIS WAS DUE TO YAW DAMPER SWITCH BEING OFF. AT THIS POINT; I SUSPECT THE PITOT HEAT SWITCHES MAY HAVE ALSO BEEN OFF; BUT WE HAD NO INDICATION. DURING TKOF ROLL; ENG CAUTION LIGHT ILLUMINATED DUE TO EEC IN ALTERNATE MODE. PASSING 10000 FT; I PRESSED RECALL PRIOR TO INITIATING THE EEC ALT MODE CHKLIST. ONLY THE ENG LIGHT REMAINED ON. BEFORE I COULD ACCOMPLISH THE CHKLIST; SINGLE FMC OPS MESSAGE APPEARED. THIS WAS FOLLOWED BY ALT AND INDICATED AIRSPD DISAGREEMENT ALERTS. I PERFORMED THE FMC FAIL CHKLIST WITH NO EFFECT. FO'S INSTS MATCHED STANDBY; WHICH CTR CONFIRMED WERE CORRECT. I THEN PERFORMED THE EEC ALT MODE CHKLIST. I LOOKED AT THE ALT AND INDICATED AIRSPD DISAGREEMENT CHKLISTS. SINCE WE HAD A DUAL FAILURE AND NEITHER CHKLIST MENTIONED A FAILURE OF THE OTHER SYS; I ASSUMED THEY WOULD NOT APPLY TO OUR SIT. HAD I PERFORMED THE INDICATED AIRSPD DISAGREEMENT AND AIRSPD UNRELIABLE CHKLISTS; WE MAY HAVE DISCOVERED SOONER THAT A LACK OF PITOT HEAT WAS CAUSING THE ERRONEOUS INDICATIONS. AFTER DISCUSSIONS WITH MAINT CTL AND DISPATCH; I DECIDED TO RETURN TO SEA. TO DETERMINE WHAT SYS I WOULD HAVE AVAILABLE FOR APCH; I AGAIN PRESSED RECALL. THIS TIME BOTH ANTI-ICE AND ENG LIGHTS REMAINED ON. NOW ALL 8 PITOT CAUTION LIGHTS WERE ON. PITOT HEAT SWITCHES WERE OFF. PLACING THEM ON RESTORED ALL SYS INCLUDING THE EEC. THE ELEVATOR DIFFERENTIAL FEEL LIGHT CAME ON DURING SUBSEQUENT RECALL; BUT SOON EXTINGUISHED. WITH MAINT AND DISPATCH CONCURRENCE; I CONTINUED ON TO IAD. I BASED THIS DECISION ON THE PITOT HEAT CAUTION BEING THE ONLY MALFUNCTIONING SYS. SINCE THE PITOT HEAT CAUTION NOW FUNCTIONED NORMALLY; I ATTRIBUTED THE FAILURE TO A TRANSIENT CONDITION CAUSED BY THE PWR INTERRUPTION AFTER START. SUPPLEMENTAL INFO FROM ACN 639219: PREFLT; PUSH AND START WERE NORMAL. AFTER ENG START; THE CAPT CALLED FOR THE AFTER START CHKLIST AND WE COMPLETED OUR FLOWS. I READ THE CHKLIST WHILE HE CONFIRMED THE SWITCHES. HE THEN TURNED THE APU OFF PRIOR TO SELECTING GENERATORS FOR A PWR SOURCE WHICH CAUSED A PWR INTERRUPTION. HIS NORMAL FLOW PATTERN WAS MODIFIED WITH THE SELECTION OF ENG ANTI-ICE PER WX CONDITIONS. TAXI WAS NORMAL WITH NUMBERS COMING LATE. I BRIEFED THE TKOF AND THEN PERFORMED THE TAXI CHKLIST WHEN THE CAPT CALLED FOR IT. ON RECALL; WE DID HAVE A FLT CTL LIGHT ONLY AND THIS WAS CORRECTED WITH THE SELECTION OF THE YAW DAMPER WHICH WAS KICKED OFF WITH THE PWR INTERRUPTION. ON TKOF ROLL; WE RECEIVED A MASTER CAUTION WITH AN ENG LIGHT. THE CAPT PERFORMED A COCKPIT CHK FOR AMBER LIGHTS AND ENG INDICATIONS; NONE WERE PRESENT WITH NORMAL INDICATIONS SO HE CALLED TO CONTINUE. ON CLBOUT; WE DISCOVERED THE EEC'S IN THE STANDBY MODE AND THE CAPT STARTED THE CHKLIST PASSING 10000 FT. SHORTLY AFTERWARDS WE RECEIVED A SINGLE FMC LIGHT WITH THE LOSS OF LNAV AND VNAV AT WHICH POINT THE CAPT PERFORMED THAT CHKLIST WHILE I MAINTAINED ASSIGNED ROUTING AND ALT. AFTER STARTING THE SINGLE FMC CHKLIST WE RECEIVED AN ALT AND INDICATED AIRSPD DISAGREEMENT LIGHT. I DETERMINED MY AIRSPD AND ALT TO BE ACCURATE AND CONTINUED TO FLY THE ACFT WHILE THE CAPT WORKED WITH MAINT AND DISPATCH PLUS KEEPING THE PAX AND FLT ATTENDANT ADVISED. WITH THE NUMEROUS MALFUNCTIONS IT WAS DECIDED TO RETURN TO SEATTLE. THE CAPT THEN STARTED THE CLEAN-UP ITEMS AND INITIATED RECALL AT WHICH TIME HE RECEIVED AN ANTI-ICE LIGHT PLUS FOR THE FIRST TIME L/R PITOT PROBE HEAT LIGHTS WITH THE SWITCHES IN THE 'OFF' POS. TURNING PITOT SWITCHES ON RESTORED ALL SYS. WITH MAINT AND DISPATCH CONCURRENCE AND VFR WX AT IAD; IT WAS DECIDED TO CONTINUE TO DEST AND TO WRITE UP THE PITOT HEAT WARNING SYS. LESSONS LEARNED: LOOK UP FROM THE CHKLIST WHEN READING TO REASSURE THAT PROPER CHK IS ACCOMPLISHED. ALSO; THE NUMEROUS MALFUNCTIONS DISGUISED THE REAL PROB; FOR IF WE HAD ONLY RECEIVED THE INDICATED AIRSPD DISAGREEMENT LIGHT; WE WOULD HAVE RUN THE AIRSPD UNRELIABLE CHKLIST THAT WOULD HAVE RESOLVED THE PROB IN A MUCH MORE TIMELY MANNER.