ACR MLG EXPERIENCED SEVERAL COMPRESSOR STALLS DURING TKOF RUN FROM LGA.

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FLT OPERATED LGA TO MSP AS AN MLG ON THE NIGHT OF 1/MON/88 WITH A DEADHEADING CREW ON BOARD. THE WX WAS IMC WITH MODERATE TO HEAVY SNOW; THE TEMP WAS 33 DEGS F. I REQUESTED FOR THE ACFT TO BE DEICED. THE F/O AND MYSELF MADE WALKAROUNDS; EVERYTHING WAS NORMAL EXCEPT THAT SNOW HAD LODGED AROUND THE BRAKE ASSEMBLY OF THE MAIN GEAR AND NOSE WHEEL AREAS. I ADVISED THE LGA OPS THAT I WOULD LIKE THE DEICING CREW TO DEICE THOSE AREAS ALONG WITH THE WHOLE ACFT. WE TAXIED OUT AND SPENT 20 MINS IN GETTING TO THE RWY (13/31). WE WERE #2 FOR DEP; ACR Y; AN MLG; WAS #1. I OBSERVED A LARGE ACCUMULATION OF SNOW ON THE TAIL OF THAT ACFT. AT ABOUT THE SAME TIME THE F/O OF THE DEADHEADING CREW CAME FORWARD; WITH MY PERMISSION; TO ADVISE ME OF THE SNOW ACCUMULATION ON OUR WINGS. I LOOKED FOR MYSELF AND INSTRUCTED THE F/O TO REQUEST A RETURN TO THE GATE FOR FURTHER DEICING. BACK IN THE GATE I AGAIN ASKED OPS TO HAVE THE DEICING CREW CHK THE WHEEL ASSEMBLIES FOR SNOW PACKING AND TO DEICE. WE DEPARTED THE GATE AGAIN AND PROCEEDED TO RWY 13. AS I ACCELERATED DOWN THE RWY I NOTICED 2 HESITATIONS OF ACCELERATION. I THOUGHT THAT IT WAS THE SNOW DISLODGING FROM THE WHEEL AREAS AND THE WHEELS RUNNING OVER SAME. AFTER WE BECAME AIRBORNE THE TWR CTLR ASKED; '(ID); ARE YOU OK?' WE RPTED; 'YES; WE ARE FINE.' THE OPERATION WAS NORMAL AND A LNDG WAS MADE AT MSP. ABOUT 1 1/2 HRS INTO THE FLT THE CAPT OF THE DEADHEADING CREW ASKED PERMISSION TO SPEAK TO ME. I GRANTED HER ENTRANCE INTO THE COCKPIT. SHE INFORMED ME THAT AS I TOOK THE RWY FOR DEP AND PUT ON THE LNDG LIGHTS SHE COULD SEE SNOW COMING OFF THE TRAILING EDGE OF THE WING AND SNOW SLIDING BY THE WINDOWS. SHE ALSO INFORMED ME AT THAT TIME THAT THERE WERE 2 LOUD BANGING SOUNDS NEAR THE ENG AREAS. AT THAT TIME ONE OF THE DEADHEADING F/A'S IN THE CABIN YELLED OUT; 'PREPARE FOR IMPACT.' LATER MY #1 F/A EXPRESSED TO ME SHE THOUGHT WE WERE GOING IN. WE LANDED AT MSP AND I HAD MAINT LOOK OVER THE ENGS AND ALSO NOTIFIED FLT CTL. I CALLED LGA TWR LONG DISTANCE AND TALKED TO THE TWR SUPVR. HE SAID HE OBSERVED 2 BRIGHT FLAMES COMING FROM THE REAR OF OUR 2 ENGS. HE IMMEDIATELY CLOSED RWY 13 AND CALLED DEP CTL TO SEE IF WE WERE AIRBORNE AND IN RADAR CONTACT. HE SAID HE WAS READY TO ALERT EMER PERSONNEL AND EQUIP IF HE DID NOT GET A POSITIVE RPT FROM DEP CTL. PS: I WOULD LIKE TO SEE A FOLLOW-UP ON MY RPT; PLEASE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: THE RWY HAD BEEN PLOWED EARLIER BUT IT WAS STILL SNOWING. AT THE TIME OF TKOF THERE WAS A BRIEF LET UP IN THE SNOW FALL AND RWYS 4/22 WERE CLOSED FOR SNOWPLOW OPERATION. THE TKOF RUN WAS CONSIDERABLY LONGER THAN NORMAL AND THE DEADHEAD CAPT RPTED HEARING 8-9 COMPRESSOR STALLS. RPTR RESTATED THAT HE NOTED SOME HESITATION DURING TKOF ROLL; BUT THOUGHT IT BECAUSE OF THE SNOW PACK BTWN THE TIRES BEING THROWN AHEAD OF THE ACFT AND CREATING AN OBSTACLE. NOTE ON RPT REQUESTING A FOLLOW-UP WAS ADDRESSED TO THE COMPANY AND NOT ASRS.