A B737-300'S CORRODED FUEL CROSSFEED CANNON PLUG MADE THE VALVE APPEAR TO BE OPEN WHEN CLOSED. THE ASSOCIATED ENG FLAMED OUT AT FL350 AFTER ABOUT 2 MIN OF CROSSFEED OPERATION. AN EMER WAS DECLARED.

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THE EMER STARTED WITH A DISCREPANCY ON THE #1 TANK CONTINUING TO DECREASE IN QUANTITY ALONG WITH THE #2 TANK WHEN SET UP FOR NORMAL XFER. I CALLED THIS SITUATION TO THE ATTN OF THE FO WHO VERIFIED BOTH THE SETUP OF THE FUEL PANEL AND THE UNUSUAL CONSUMPTION OUT OF THE L TANK. THE FUEL PANEL WAS SET UP WITH THE L MAIN PUMPS OFF; R PUMPS ON; AND THE XFEED OPEN WITH A DIM BLUE LIGHT INDICATING OPEN. SUBSEQUENT VERIFICATION OF THE XFEED VALVE INDICATED NORMAL OP WITH NO CHANGE IN THE RELATIVE FUEL FLOWS TO EACH ENG. THE DIFFERENCE BTWN THE TANKS WAS APPROX 300 LBS HEAVIER ON THE #2 SIDE. APPROX 2 MINS AFTER NOTING THE ANOMALY; I NOTICED A FLUCTUATION IN THE #1 EGT OF ABOUT 30 DEGS C. IT WAS A SLOW FLUCTUATION DOWN AND THEN IT RETURNED TO NORMAL; ABOUT 350 DEGS C. THE L ENG FAILED SOON AFTER WITH A SLOW ROLL BACK AND SUBSEQUENT L YAW. I IMMEDIATELY DECLARED AN EMER AND BEGAN SLOWING TO DRIFTDOWN AIRSPD OFF THE FMC; ABOUT 220 KTS. I WAS HAND FLYING THE ACFT AS THE AUTOPLT WOULD NOT RE-ENGAGE UNTIL BELOW FL250. THE FO BROUGHT OUT THE QRH; IDENTED THE ENG FAIL CHKLIST WHICH WE RAN ACCORDINGLY. PASSING FL300; I TURNED ALL THE PUMPS ON AND CLOSED THE XFEED AS WE EVALED THE POSSIBILITY OF AN AIR START. AS N2 WAS TOO LOW FOR A WINDMILL START; WE WAITED UNTIL BELOW FL200 TO COMPLETE AN AIR-ASSISTED START. THE ENG STARTED NORMALLY AND WE ELECTED TO CONTINUE THE DIVERT TO ZZZ WITH SINGLE ENG APCH PROCS READY IF WE NEEDED THEM. DISPATCH WAS INFORMED VIA ACARS AS EARLY AS POSSIBLE AND THEY CONCURRED WITH ZZZ AS A DIVERT. THE APCH AND LNDG WERE NORMAL. AFTER LNDG I HAD THE ZZZ FIRE CREWS INSPECT THE L MOTOR FOR DAMAGE OR LEAKS AND NONE WERE SEEN. I DOCUMENTED THE ENG FAILURE IN THE LOGBOOK ALONG WITH A DESCRIPTION OF NOTED ANOMALIES. IF AIRCREWS SEES ABNORMAL XFER INDICATIONS; STOP THE XFER IMMEDIATELY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE REPORTER STATED THAT AFTER MAINTENANCE EXAMINED THE ACFT; THEY FOUND THAT A CORRODED CROSSFEED VALVE CANNON PLUG DID NOT ALLOW THE CROSSFEED VALVE TO OPEN EVEN THOUGH THE COCKPIT CROSSFEED VALVE LIGHT INDICATED IT TO BE OPEN. ABOVE FL300 THE ENG FUEL PUMP DOES NOT HAVE ENOUGH SUCTION TO FEED THE ENG. IN THIS CASE AFTER ABOUT 2 MINUTES OF TOO LITTLE FUEL FROM THE TANK THE ENG FLAMED OUT. MAINTENANCE TOLD THE REPORTER THAT EVEN IF THE CREW HAD KNOWN THAT THE CROSSFEED DID NOT OPEN; THE ENG PROBABLY WOULD HAVE FLAMED OUT WHEN THE PUMPS WERE TURNED ON BECAUSE OF THE EVACUATED FUEL LINES AND TIME REQUIRED TO RE-PRESSURIZE THEM.